CN115629606A

CN115629606A - Following control method and device for vehicle under countermeasure information, vehicle and storage medium

Info

Publication number: CN115629606A
Application number: CN202211267448.0A
Authority: CN
Inventors: 刘艺璁; 王建强; 许庆; 蔡孟池; 王映焓
Original assignee: Tsinghua University
Current assignee: Tsinghua University
Priority date: 2022-10-17
Filing date: 2022-10-17
Publication date: 2023-01-20

Abstract

The application relates to the technical field of intelligent networked automobiles, in particular to a vehicle following control method and device under countermeasure information, a vehicle and a storage medium, wherein the method comprises the following steps: establishing a control system model of the vehicle according to the countermeasure information of the vehicle, decoupling the calculation of the vehicle state reachable set into the calculation of the vehicle difference reachable set and the determination of the vehicle reference track variable by combining the linear state feedback control law, thus iteratively solving the mathematical expression of the vehicle difference reachable set, optimizing the linear state feedback control law and solving to obtain an optimal feedback matrix sequence; and calculating a difference reachable set after the optimization of the vehicle at each moment to obtain a corresponding numerical vector, coupling the vehicle reference track vector with the numerical vector, and calculating to obtain a final difference reachable set so as to realize the prediction of the vehicle following track at the next moment. Therefore, the problems that the reachable set calculation method in the related technology is low in calculation efficiency, over-approximate calculation is performed, optimization of the reachable set is not involved and the like are solved.

Description

Following control method and device for vehicle under countermeasure information, vehicle and storage medium

Technical Field

The application relates to the technical field of intelligent networked automobiles, in particular to a vehicle following control method and device under countermeasure information, a vehicle and a storage medium.

Background

In the future, the car networking environment will make the control system of the intelligent car more vulnerable to information-fighting attacks, for example, a type of integrity attack, i.e., an attack by intentionally modifying control instructions or sensing data. Specifically, when the future intelligent networked automobiles share computing resources and a control platform, the automobiles can be regarded as a remote control system, the automobiles are controlled by receiving wireless control instructions, and the countermeasure information can be modification or injection of automobile control data. The existence of such countermeasure information will affect the vehicle state, thereby affecting the safety of vehicle control, and it is difficult to completely resist the intrusion of the countermeasure information only based on the communication detection mechanism, so that the calculation and optimization of the reachable set of the vehicle state under the countermeasure information can quantitatively describe the influence range of the countermeasure information on the vehicle state, which is the basis and precondition for realizing the safety of vehicle control.

The vehicle reachability analysis generally refers to determination and classification of state quantities that may occur in the future at various times of the vehicle control system, and a set of all the state quantities that may occur at each time is a state reachability set. At present, most of mathematical descriptions of state reachable sets are based on a multicorpuscle (Polytope) set, a fully-symmetrical multicorpuscle (Zontope) set, an Ellipsoid (Ellipsoid) set and a Multidimensional interval shape (Multidimentional interval) set, and reachable set calculation methods mainly comprise methods such as value functions and decoupling iteration and have the problems of low calculation efficiency, over-approximate calculation and the like.

Disclosure of Invention

The application provides a vehicle following control method and device under countermeasure information, a vehicle and a storage medium, and aims to solve the problems that the reachable set calculation method in the related art is low in calculation efficiency, over-approximate calculation is performed, and optimization of a reachable set is not involved.

An embodiment of a first aspect of the application provides a vehicle following control method for a vehicle under countermeasure information, which includes the following steps: acquiring preset countermeasure information of a vehicle; establishing a control system model of the vehicle according to the preset reactance information, and decoupling the control system model by adopting a preset linear state feedback control law to obtain a reference track state quantity and an initial difference reachable set of the vehicle at each preset moment after the current moment; iteratively calculating an initial difference reachable set at each preset moment to obtain a difference reachable set expression of the vehicle, optimizing the preset linear state feedback control law based on the difference reachable set expression, and solving to obtain an optimal feedback matrix sequence based on the optimized preset linear state feedback control law; iteratively calculating an initial difference reachable set of each preset moment based on the optimal feedback matrix sequence and the optimized preset linear state feedback control law to obtain a numerical vector of each preset moment; and coupling the numerical vector and the reference track state quantity at each preset moment to obtain a final difference reachable set, predicting a following track of the vehicle at the next moment based on the final difference reachable set, and controlling the vehicle to run along the following track.

Optionally, in an embodiment of the present application, the establishing a control system model of the vehicle according to the preset reactance information includes: taking the preset reactance information as the input of a preset continuous linear system of the vehicle; carrying out abstract modeling and analysis on longitudinal dynamics and transverse dynamics of the vehicle based on the preset linear system to obtain a dynamic model of the vehicle; discretizing the dynamic model to obtain a discretization system model, and determining the property and the boundary of the preset reactance information to obtain the control system model.

Optionally, in an embodiment of the application, the decoupling the control system model by using a preset linear state feedback control law to obtain a reference trajectory state quantity and an initial difference reachable set of the vehicle at each preset time after the current time includes: acquiring a reference track control quantity and an actual state quantity of the vehicle; inputting the reference track control quantity into the control system model for iterative update to obtain a reference track state quantity of the vehicle at each preset moment; and calculating the differential state quantity of the vehicle according to the offset of the reference track state quantity, iteratively updating the actual state quantity and the differential state quantity according to the vehicle by utilizing the preset linear state feedback control law to obtain the differential state of the vehicle at each preset moment, and establishing the initial differential reachable set based on the differential state of the vehicle at each preset moment.

Optionally, in an embodiment of the application, the iteratively calculating the initial difference reachable set at each preset time to obtain the difference reachable set expression of the vehicle includes: performing mathematical description on the initial difference reachable and antagonistic information sets by adopting a Zontope set, and determining an iteration rule and mathematical properties of the Zontope set; performing iterative computation on the difference reachable set at the known moment according to the iteration rule and the mathematical property of the Zontope set to obtain the difference reachable set at the next moment; and determining a generated vector based on the difference reachable set of the next moment obtained by iterative computation, and obtaining the expression of the difference reachable set of the vehicle according to the generated vector.

Optionally, in an embodiment of the application, the optimizing the preset linear state feedback control law based on the differential reachable set expression, and solving to obtain an optimal feedback matrix sequence based on the optimized preset linear state feedback control law includes: iteratively calculating a dynamic feedback matrix sequence variable based on the difference reachable set expression; optimizing the preset linear state feedback control law according to the dynamic feedback matrix sequence variable to obtain the optimized preset linear state feedback control law; and constructing an optimization problem of the space size and the shape of a difference reachable set according to a preset standard static feedback control law, and solving the optimization problem based on the preset linear state feedback control law to obtain the optimal feedback matrix sequence.

An embodiment of a second aspect of the present application provides a following control device for a vehicle under countermeasure information, including: the acquisition module is used for acquiring preset countermeasure information of the vehicle; the processing module is used for establishing a control system model of the vehicle according to the preset reactance information and decoupling the control system model by adopting a preset linear state feedback control law to obtain a reference track state quantity and an initial difference reachable set of the vehicle at each preset moment after the current moment; the first calculation module is used for iteratively calculating an initial difference reachable set at each preset moment to obtain a difference reachable set expression of the vehicle, optimizing the preset linear state feedback control law based on the difference reachable set expression, and solving to obtain an optimal feedback matrix sequence based on the optimized preset linear state feedback control law; the second calculation module is used for iteratively calculating an initial difference reachable set of each preset moment based on the optimal feedback matrix sequence and the optimized preset linear state feedback control law to obtain a numerical vector of each preset moment; and the control module is used for coupling the numerical vector and the reference track state quantity at each preset moment to obtain a final difference reachable set, predicting a vehicle following track at the next moment of the vehicle based on the final difference reachable set, and controlling the vehicle to run along the vehicle following track.

Optionally, in an embodiment of the present application, the processing module is further configured to use the preset reactance information as an input of a preset continuous linear system of the vehicle; carrying out abstract modeling and analysis on the longitudinal dynamics and the transverse dynamics of the vehicle based on the preset linear system to obtain a dynamic model of the vehicle; discretizing the dynamic model to obtain a discretization system model, and determining the property and the boundary of the preset reactance information to obtain the control system model.

Optionally, in an embodiment of the present application, the processing module is further configured to obtain a reference trajectory control quantity and an actual state quantity of the vehicle; inputting the reference track control quantity into the control system model for iterative updating to obtain a reference track state quantity of the vehicle at each preset moment; and calculating the differential state quantity of the vehicle according to the offset of the reference track state quantity, performing iterative update on the actual state quantity and the differential state quantity according to the vehicle by using the preset linear state feedback control law to obtain the differential state of the vehicle at each preset moment, and establishing the initial differential reachable set based on the differential state of the vehicle at each preset moment.

Optionally, in an embodiment of the present application, the first computing module is further configured to mathematically describe the initial difference reachability and confrontation information sets by using a zontope set, and determine an iteration rule and a mathematical property of the zontope set; performing iterative computation on the difference reachable set at the known moment according to the iteration rule and the mathematical property of the Zontope set to obtain the difference reachable set at the next moment; and determining a generated vector based on the difference reachable set of the next moment obtained by iterative computation, and obtaining the expression of the difference reachable set of the vehicle according to the generated vector.

Optionally, in an embodiment of the present application, the first calculating module is further configured to iteratively calculate a dynamic feedback matrix sequence variable based on the differential reachable set expression; optimizing the preset linear state feedback control law according to the dynamic feedback matrix sequence variable to obtain the optimized preset linear state feedback control law; and constructing an optimization problem of the space size and the shape of a difference reachable set according to a preset standard static feedback control law, and solving the optimization problem based on the preset linear state feedback control law to obtain the optimal feedback matrix sequence.

An embodiment of a third aspect of the present application provides a vehicle, comprising: a memory, a processor and a computer program stored on the memory and operable on the processor, the processor executing the program to implement the following control method of a vehicle under countermeasure information as described in the above embodiments.

A fourth aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, the program being executed by a processor for implementing the following control method of a vehicle under countermeasure information as described in the above embodiments.

Therefore, the application has at least the following beneficial effects:

a control system model of the vehicle is established according to the countermeasure information of the vehicle, the calculation of the vehicle state reachable set is decoupled into the calculation of the vehicle difference reachable set and the determination of the vehicle reference track variable by combining a linear state feedback control law, so that the mathematical expression of the vehicle difference reachable set is obtained iteratively, a method for optimizing a dynamic feedback matrix sequence is provided, the space size and the shape of the calculated reachable set are optimized, the difference reachable set can be reduced and remolded, the control quantity limit can be ensured not to be excessively contracted, the balance relation between the existing feedback matrix and the control quantity limit is relieved to a certain extent, and basic guarantee is provided for the control safety of the vehicle in the following scene. Therefore, the problems that the reachable set calculation method in the related technology is low in calculation efficiency, over-approximate calculation is performed, optimization of the reachable set is not involved and the like are solved.

Additional aspects and advantages of the present application will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the present application.

Drawings

The foregoing and/or additional aspects and advantages of the present application will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:

fig. 1 is a flowchart of a following control method for a vehicle under countermeasure information according to an embodiment of the present application;

FIG. 2 is a schematic diagram of vehicle state reachable set decoupling and coupling provided in accordance with an embodiment of the present application;

fig. 3 is a schematic view illustrating driving of a following front vehicle of a vehicle following scene remotely controlled according to an embodiment of the application;

FIG. 4 is a schematic illustration of a controlled vehicle platform provided in accordance with an embodiment of the present application;

FIG. 5 is a schematic diagram of a vehicle model for integrity countervailing information attack according to an embodiment of the present application;

FIG. 6 is a flow chart illustrating a vehicle state reachable set calculation and control optimization according to an embodiment of the present disclosure;

FIG. 7 is a model diagram of a vehicle control system for a car following scene according to an embodiment of the present disclosure;

fig. 8 is a schematic diagram of iterative computation of a difference reachable set Jing Cheliang according to the present embodiment;

fig. 9 is a schematic diagram illustrating comparison of optimization of a difference reachable set 5363 with a yard Jing Cheliang according to an embodiment of the present application;

fig. 10 is a block diagram illustrating a vehicle following control apparatus of a vehicle under countermeasure information according to an embodiment of the present application;

fig. 11 is a schematic structural diagram of a vehicle according to an embodiment of the present application.

Description of reference numerals: the device comprises an acquisition module-100, a processing module-200, a first calculation module-300, a second calculation module-400, a control module-500, a memory-1101, a processor-1102 and a communication interface-1103.

Detailed Description

Reference will now be made in detail to embodiments of the present application, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are exemplary and intended to be used for explaining the present application and should not be construed as limiting the present application.

A following control method and apparatus for a vehicle under countermeasure information, a vehicle, and a storage medium according to embodiments of the present application are described below with reference to the drawings. In order to solve the problems mentioned in the background art, the application provides a vehicle following control method under countermeasure information, in the method, a control system model of a vehicle is established according to the countermeasure information of the vehicle, calculation of a vehicle state reachable set is decoupled into calculation of a vehicle difference reachable set and determination of a vehicle reference track variable by combining a linear state feedback control law, so that a mathematical expression of the vehicle difference reachable set is obtained iteratively, a method for optimizing a dynamic feedback matrix sequence is provided, the space size and the shape of the calculated reachable set are optimized, the difference reachable set can be reduced and reshaped, the control quantity limit is ensured not to be excessively tightened, the balance relation between the existing feedback matrix and the control quantity limit is relieved to a certain extent, and basic guarantee is provided for realizing control safety of the vehicle under a vehicle following scene. Therefore, the problems that the reachable set calculation method in the related technology is low in calculation efficiency, over-approximate calculation is performed, optimization of the reachable set is not involved and the like are solved.

Specifically, fig. 1 is a schematic flow chart of a following control method of a vehicle under countermeasure information according to an embodiment of the present application.

As shown in fig. 1, the following control method of the vehicle under the countermeasure information includes the steps of:

in step S101, preset countermeasure information of the vehicle is acquired.

In the embodiment of the present application, the preset countermeasure information may be integrity countermeasure information.

It can be understood that most of the existing reachable set calculation methods do not combine the classical state feedback control law of the vehicle, and few optimization problems related to the reachable set exist. The embodiment of the application can be improved and perfected on the basis of the existing method, and by acquiring the countermeasure information of the vehicle, a calculation and optimization method of the reachable set of the vehicle state is established aiming at the situation that one type of completeness countermeasure information attacks the vehicle, so that the method is more suitable for reachability analysis and control optimization of the intelligent networked automobile under the countermeasure information.

In step S102, a control system model of the vehicle is established according to the preset reactance information, and a reference trajectory state quantity and an initial difference reachable set of the vehicle at each preset time after the current time are obtained by using a preset linear state feedback control law decoupling control system model.

It can be understood that, according to the embodiment of the application, a vehicle control system can be modeled according to the countermeasure information of a vehicle, a linear state feedback control law is adopted, the calculation of a vehicle state reachable set is decoupled into the determination of vehicle differential state reachability analysis and vehicle reference track variables, and according to an iterative update rule, the reference track state quantity and the vehicle differential state quantity at any subsequent time can be calculated from the current time.

In one embodiment of the present application, building a control system model of a vehicle according to preset reactance information includes: using preset reactance information as an input of a preset continuous linear system of the vehicle; abstract modeling and analyzing longitudinal dynamics and transverse dynamics of the vehicle based on a preset linear system to obtain a dynamic model of the vehicle; and discretizing the discretization dynamic model to obtain a discretization system model, and determining the property and the boundary of preset resistance information to obtain a control system model.

Specifically, the embodiment of the application can model the vehicle control system according to the integrity countermeasure information of the vehicle, and comprises the following steps:

s11, firstly, establishing a vehicle dynamic model by using a continuous linear system. Under normal working conditions, the linear system can carry out abstract modeling and analysis on longitudinal dynamics and transverse dynamics of the intelligent networked vehicle, as shown in the following formula (1).

Wherein t is the current time point;

is a state vector of the vehicle control system;

inputting control quantity of the system;

inputting countermeasure information for the system; a. The _cont For the continuous system matrix, B _cont And C _cont The matrix may be time-variant or time-invariant for the system input matrix.

And S12, discretizing the continuous vehicle dynamic system. In practical applications, since the vehicle control command is updated and executed discretely at a frequency of 10Hz in many cases, a discrete system can be obtained by discretizing a continuous system with a sample time by a zero-order keeper, as shown in the following equation (2).

x(k+1)＝Ax(k)+Bu(k)+Cw(k) (2)

Wherein, the first and the second end of the pipe are connected with each other,

is the current discrete time; a is the discrete system matrix, B and CThe system input matrix can be calculated by the following equations (3), (4) and (5).

Wherein T is the sampling time.

And S13, determining the nature and the boundary of the countermeasure information. Countermeasure information is an input to the vehicle dynamics system other than the control quantity, and is generally bounded on engineering. The countermeasure information is not preset with prior information within the boundary, but is arbitrary and infinitely possible. According to the related art, the bounding property of the countermeasure information is defined as norm bounding, and the bounding property can be expressed as shown in the following formula (6) taking an infinite norm as an example.

Wherein the content of the first and second substances,

is a known quantity for the upper bound of countermeasure information.

It should be noted that, after modeling the vehicle control system, as shown in formula (2), the system state x will inevitably be affected by both the control quantity u and the countermeasure information w; the control quantity u is a vehicle control quantity (unknown but controllable) given by the remote control center, but the countermeasure information w is bounded and uncertain (unknown and uncontrollable), so the system state x is uncertain under the influence of the countermeasure information w, and the reachability analysis is to analyze what range the system state x may be in at each future time or what the uncertainty of the system state x is.

In an embodiment of the present application, obtaining a reference trajectory state quantity and an initial difference reachable set of a vehicle at each preset time after a current time by using a preset linear state feedback control law decoupling control system model includes: acquiring a reference track control quantity and an actual state quantity of a vehicle; inputting the reference track control quantity into a control system model for iterative updating to obtain a reference track state quantity of the vehicle at each preset moment; and calculating the differential state quantity of the vehicle according to the offset of the reference track state quantity, performing iterative update on the actual state quantity and the differential state quantity according to the vehicle by using a preset linear state feedback control law to obtain the differential state of the vehicle at each preset moment, and establishing an initial differential reachable set based on the differential state of the vehicle at each preset moment.

Specifically, the embodiment of the application can decouple the calculation of the vehicle state reachable set into the determination of the vehicle differential state reachability analysis and the vehicle reference track variable, and comprises the following steps:

and S21, establishing a vehicle reference track variable. As shown in fig. 2, assuming that a virtual reference track exists as a tracking target of the vehicle system, and the initial state of the virtual reference track is known, the state quantities of the reference track are continuously updated iteratively as time changes, as shown in the following equation (7).

x _ref (k+1)＝Ax _ref (k)+Bu _ref (k) (7)

Wherein x is _ref The initial state of the reference track state vector used for tracking is consistent with the current vehicle state and is a known quantity; u. of _ref Is a reference trajectory control quantity for tracking.

The reference trajectory in a period of time is composed of the reference trajectory state quantities at each time, and in the case of the known initial state, the reference trajectory state quantity at any time is determined only by all the previous reference trajectory control quantities according to the above iterative relationship, as shown in the following equation (8).

x _ref (k)＝F _ref-iter (u _ref (0)，u _ref (1)，…，u _ref (k-1)) (8)

Wherein, F _ref-iter The relationship is iterated for the reference trajectory state based on equation (7).

Therefore, the virtual reference trajectory can be uniquely determined by a set of reference trajectory control quantity sequences.

And S22, converting the original problem into reachability analysis of the vehicle differential state quantity in a linear state feedback control law mode. Feedback control can improve the control performance of the system, and the embodiment of the application can combine a classical linear feedback control law with the calculation of a vehicle state reachable set, wherein the linear feedback control law is shown as the following formula (9).

u(k)＝u _ref (k)+K[x(k)-x _ref (k)] (9)

Wherein, K is a linear state feedback matrix and is time-varying or time-invariant.

In conjunction with the vehicle actual state quantity, an iterative update rule of the deviation amount of the vehicle actual state quantity from the reference trajectory state quantity (i.e., the vehicle differential state quantity) over time can be obtained as shown in the following equations (10) (11).

x _d (k)＝x(k)-x _ref (k) (10)

x _d (k+1)＝(A+BK)x _d (k)+Cw(k) (11)

Wherein x is _d As a differential state quantity of the vehicle, an initial differential state quantity x _d (0) Is a zero vector.

When the initial differential state is known, the differential state quantity at any time is determined only by all the countermeasure information, and is independent of the vehicle reference trajectory variable, according to the above iterative relationship, as shown in the following equation (12).

x _d (k)＝F _d-iter (w(0)，w(1)，…，w(k-1)) (12)

Wherein, F _d-iter Is a differential state iterative relationship based on equation (11).

Therefore, the original problem about the calculation of the vehicle state reachable set can be converted into the calculation of the vehicle difference state reachable set, and the calculation is relatively independent of the determination of the vehicle reference track variable.

It should be noted that the state reachable set in the embodiment of the present application is caused by bounded but uncertain countermeasure information w, and the system state x is a set consisting of all possible vector values that may occur at each time in the future, and a shaded area in fig. 2.

In step S103, an initial difference reachable set at each preset time is iteratively calculated to obtain a difference reachable set expression of the vehicle, a preset linear state feedback control law is optimized based on the difference reachable set expression, and an optimal feedback matrix sequence is obtained by solving based on the optimized preset linear state feedback control law.

It can be understood that, in the embodiment of the present application, under the condition that a differential reachable set at the previous time is known, the differential reachable set at the next time can be efficiently calculated, so as to obtain a differential reachable set expression of the vehicle, rolling iterative computation of the reachable set is performed in combination with vehicle state feedback control, and a method for optimizing a dynamic feedback matrix sequence is provided, so that the spatial size and the shape of the calculated reachable set are optimized, and the embodiment of the present application can better serve for security control of the intelligent internet-connected vehicle under the influence of countermeasure information.

In one embodiment of the present application, iteratively calculating the initial difference reachable set at each preset time to obtain a difference reachable set expression of the vehicle, includes: carrying out mathematical description on the initial difference reachable and antagonistic information sets by adopting a Zontope set, and determining an iteration rule and mathematical properties of the Zontope set; performing iterative computation on the difference reachable set at the known moment according to the iteration rule and the mathematical property of the Zontope set to obtain the difference reachable set at the next moment; and determining a generated vector based on the difference reachable set of the next moment obtained by iterative computation, and obtaining the expression of the difference reachable set of the vehicle according to the generated vector.

The method for describing the Zontope set-based multi-dimensional space convex set is mainly characterized in that a region is generated in the space through a central vector and a series of generated vectors, the region is the Zontope set, iterative calculation of the set can be efficiently carried out through the set description method, and an optimization problem can be built through extracting elements of the generated vectors of all reachable sets so as to reduce and reshape the calculated and optimized reachable sets.

Further, the embodiment of the application can iteratively solve the mathematical expression based on the Zontope vehicle difference reachable set, and the method comprises the following steps:

and S31, mathematically describing the vehicle initial difference reachable and confrontation information sets by adopting a Zontope set. The mathematical expression of Zontope set Z in a space is shown in equation (13) below.

Wherein, c _z Is a central vector representing the center of the set Z; g is a radical of formula ⁽¹⁾ ,L,g ^(e) Generating a vector for the series of sets Z; beta is a _i Represents [ -1,1]Any real number within the range.

For simplification, the set Z can be simply expressed as the following formula (14).

Z＝(c _z ，<g ⁽¹⁾ ，g ⁽²⁾ ，…，g ^(e) >) (14)

From the mathematical expression of the Zontope set, it can be known that the linear transform (matrix left-multiplication) operation and the Minkowski sum (Minkowski sum) operation still belong to the Zontope set.

Considering that a random error may exist in the sensing and positioning system of the intelligent networked automobile, that is, an observation error exists in the vehicle state, the initial difference reachable set of the vehicle is no longer a zero vector, but is a spatial set, which is described as a zontope set with a center vector being a zero vector, as shown in the following formula (15).

Wherein S is ^d The initial difference reachable set is a vehicle, and the difference reachable set is a Zonotope set.

The infinite norm bounded countermeasure information given by equation (6) can also be described as a zontoppe set whose center vector is a zero vector, as shown in equation (16) below.

Wherein D is _w The countermeasure information for the vehicle is a bounded set, zontope set.

And S32, iteratively calculating the vehicle difference reachable set at each moment. According to the iteration rule described in equation (11) and the mathematical property of the zontoppe set, given the difference reachable set at the previous time, the difference reachable set at the next time can be efficiently calculated, as shown in equation (17) below.

is the difference reachable set at time k; reach is an iterative computation function of the reachable set;

the linear transformation operator is expressed and can be directly acted on each vector of the Zontope set;

representing the minkowski sum operator, can be computed by a one-time vector addition (two central vectors) and a concatenation of two linked lists (two sets of generated vectors), with computational efficiency.

From this, the reachable set of vehicle differences at each time in the future can be iteratively calculated, and all are Zonotope sets, as shown in equation (18) below.

representing the difference reachable set of the time N, if the feedback matrix K is a variable, the generated vector of the difference reachable set is inverseA functional expression of the feed matrix K.

In an embodiment of the present application, optimizing a preset linear state feedback control law based on a differential reachable set expression, and solving to obtain an optimal feedback matrix sequence based on the optimized preset linear state feedback control law, includes: iteratively calculating a dynamic feedback matrix sequence variable based on the difference reachable set expression; optimizing a preset linear state feedback control law according to the dynamic feedback matrix sequence variables to obtain the optimized preset linear state feedback control law; and constructing an optimization problem of the space size and the shape of the difference reachable set according to a preset standard static feedback control law, and solving the optimization problem based on a preset linear state feedback control law to obtain an optimal feedback matrix sequence.

Specifically, the embodiment of the application can optimize the linear state feedback control law and solve the corresponding feedback matrix sequence based on the vehicle difference reachable expression, and comprises the following steps:

and S41, introducing dynamic feedback matrix sequence variables to optimize a feedback control law. The linear feedback control law described by equation (9) will contain feedback matrix variables as shown by equation (19) below.

u(k)＝u _ref (k)+K(k)[x(k)-x _ref (k)] (19)

And K (K) represents a feedback matrix variable at the moment K and is to be optimized and solved.

At this time, equation (18) iteratively calculates that the vehicle difference reachable set at each time in the future contains feedback matrix variables K (0), K (1), L, K (N-1) at each time.

And S42, constructing an optimization problem about the size and the shape of the difference reachable set space for the standard static feedback control law. The existing reachability analysis method combining linear feedback control is mostly based on a static feedback matrix, for example, a linear quadratic regulator is used for obtaining the static feedback matrix K _lqr 。

On the basis, the embodiment of the application can realize two optimization targets, namely reducing the differential reachable set caused by the countermeasure information and reshaping the shape of the differential reachable set according to the constraint characteristics; and to ensure a precondition that the reference trajectory control quantity limit is not excessively tightened. The optimization problem was constructed as shown in the following formulas (20) (21).

Wherein K (-) represents a feedback matrix variable K (-) which is an optimization variable;

a weight matrix for each dimension for reshaping the set shape;

a vector is generated for the jth of time instant k.

The selection of the weight matrix in the optimization problem can be carried out without distinguishing on each dimension, and the value is omega _k ＝[1 1 1] ^T (ii) a And values can be taken according to the extreme value difference (extreme change range) of the constraint set in the scene of following the vehicle in each dimension, so that the shape of the optimized reachable set is closer to the constraint set, and the control safety of the vehicle is conveniently realized, as shown in the following formula (21.5).

Wherein D is a generation vector

Dimension of (d);

for a maximum in the ith dimension of the state constraint set,

the minimum value in the ith dimension is constrained for the state.

The constructed optimization problem is represented in an optimization target by the sum of the absolute values of all generated vectors at each moment under the influence of each dimension weight, and reflects the size of the set and reshapes the shape of the set; the constraint condition is embodied in that the control quantity consumed by the optimized linear feedback control law in the feedback process at each moment is not more than that before optimization, namely under the condition that the total control quantity is bounded, the control quantity limit of the optimized reference track is not less than that before optimization.

And S43, solving the optimized dynamic feedback matrix sequence, and updating the optimized control law. Selecting an optimization algorithm (such as Newton method, interior point method and the like), solving the optimization problem represented by the formula (20) and the formula (21) to obtain an optimal feedback matrix sequence K ^* (0),K ^* (1),L,K ^* (N-1), the feedback matrix at each moment is substituted for the linear feedback control law described in equation (19) to obtain an optimized control law, as shown in equation (22) below.

u(k)＝u _ref (k)+K ^* (k)[x(k)-x _ref (k)] (22)

In step S104, an initial difference reachable set at each preset time is iteratively calculated based on the optimal feedback matrix sequence and the optimized preset linear state feedback control law to obtain a numerical vector at each preset time.

In the embodiment of the application, step S32 may be executed again according to the obtained optimal feedback matrix sequence and the optimized control law, and the difference reachable set of the vehicle at each moment is subjected to numerical iterative computation, and is subjected to numerical computation to obtain the difference reachable set described by zontope, as shown in formula (18). The difference from the first execution of step S32 is that all vectors of the difference reachable set at each time are numerical vectors instead of expressions with the feedback matrix K as a variable.

In step S105, a final difference reachable set is obtained by coupling the value vector and the reference trajectory state quantity at each preset time, a following trajectory of the vehicle at a next time is predicted based on the final difference reachable set, and the vehicle is controlled to travel along the following trajectory.

Specifically, the vehicle reference track and the difference reachable set can be coupled, and the state reachable set after vehicle optimization at each future moment is obtained through calculation. First, according to equation (10), the vehicle actual state reachable set is determined by the reference trajectory state and the differential reachable set, and is a coupling between the reference trajectory state and the differential reachable set, as shown in equation (23).

Wherein R is _k The reachable set of vehicle states at time k.

Next, a reachable set of vehicle states described by zontope at each time in the future is obtained according to equation (18), as shown in equation (24).

Wherein R is _N A reachable set of vehicle states representing time N; the central vector of each set is the reference trajectory state vector at the corresponding time.

Therefore, the vehicle state reachable set optimized at each future time is obtained according to the embodiment of the application and is presented in the form of the Zonotope set. According to the one-to-one correspondence described by the formula (7) and the formula (8), the reachable set of the vehicle state at each moment is only a function of the reference track (state quantity or control quantity), the influence range of the countermeasure information on the vehicle state is quantitatively described, and basic guarantee is provided for realizing the reference track planning of vehicle control safety.

In the following, a classic and common car following scenario is combined, and the calculation and control optimization of the reachable set of the vehicle state is performed by using the car following control method of the vehicle under the countermeasure information of the embodiment of the present application. As shown in fig. 3, the controlled vehicle is controlled by the remote control center in real time, runs along a straight road along with a preceding vehicle, obtains environmental information through the sensing and positioning system during running, and can communicate with the remote control center through the road side unit, and the vehicle may be attacked by a type of integrity countermeasure information during communication, so that the vehicle following state and performance of the vehicle are affected.

The controlled Vehicle is an Intelligent Internet Vehicle (Intelligent and Connected Vehicle), as shown in FIG. 4. The vehicle is provided with a high-precision Positioning System to obtain information such as vehicle position, speed, acceleration and the like, the Positioning mode can comprise a Difference Global Positioning System (DGPS) in American System, a Glonass Global Satellite Navigation System (GLONASS) in Russian System, a Galileo Global Satellite Navigation System (GALILEO) in Europe System, a BeiDou Navigation Satellite Navigation System (BDS) in China, and an Inertial Measurement Unit (IMU) and the Satellite Positioning System are introduced for data fusion in order to overcome the influence of the problems of insufficient update frequency of the Satellite Positioning System, possible instability of signals and the like on the Positioning precision, so that a faster and more accurate Positioning effect can be achieved, and a laser radar-based synchronous Positioning and map construction method (Simultaneous Localization and Mapping, SLAM) and a camera-based vision calculation method and the like can be introduced to achieve more high-precision vehicle Positioning mileage. The controlled self-vehicle is also provided with communication equipment, the adopted communication technology comprises DSRC and LTE-V, the communication range can be close to 1 kilometer, the communication time delay can be controlled within 0.1 second which is far less than a typical control period, the controlled self-vehicle can communicate with a remote control center and exchange information, as shown in figure 5, the self-vehicle packs state quantity information (such as position, speed, acceleration and the like of the self-vehicle, the position and the speed of a front vehicle) acquired by a sensing and positioning system, transmits the state quantity information to a Road Side communication Unit (RSU) in real time through the DSRC or LTE-V communication technology, and feeds back data to the remote control center through a special communication mode of the Road Side Unit and the remote control center, wherein the transmitted state quantity information senses the nonideal of the positioning system and necessarily has a certain state observation error; the remote control center calculates and optimizes a vehicle state reachable set in a vehicle following scene based on the acquired information and considering a state observation error, potential integrity countermeasures and boundaries thereof, outputs a corresponding control quantity according to vehicle state reachability analysis, and transmits the control quantity to a controlled self-vehicle based on communication equipment and technology, wherein attack of the integrity countermeasures may exist in the communication process, and the attack specifically comprises modification or injection of transmitted control quantity data.

In the embodiment of the present application, after obtaining necessary information, the remote control center performs gradual calculation by using the vehicle state reachable set calculation and control optimization method of the embodiment of the present application, as shown in fig. 6, and the calculation and optimization process includes the following steps:

s1, modeling a vehicle control system in a vehicle following scene according to a type of integrity countermeasure information.

S11, firstly, a vehicle dynamic model under a vehicle following scene is established by a continuous linear system. As shown in fig. 7, the continuous linear system model of the vehicle in the following scene can be conveniently expressed by the state space as shown in the following equations (25) (26).

x＝[s v a] ^T ,u＝a _des ,w＝a _adv (26)

Where s denotes a vehicle position (m), v denotes a vehicle speed (m/s), and a denotes a vehicle acceleration (m/s) ² ) And the three are used as the state quantity of the vehicle control system in the scene of following the vehicle; a is _des Indicates a desired acceleration (control amount input) of the vehicle, and has a boundary set to a _des ∈[-5,5]m/s ² ；a _adv Representing a bounded countermeasure information input; t is _L =0.45s is a time lag characteristic in consideration of vehicle control; k _L And =1 is the closed loop steady state gain of the vehicle control system.

And S12, discretizing a vehicle dynamic system in a vehicle following scene. Considering that the typical control frequency of the vehicle is 10Hz, discretization is performed by step length (sampling time) T =0.1s, and then the corresponding system matrix and input matrix can be calculated according to equations (3) to (5), and then the discrete dynamic system model of the vehicle in the following scene is shown as equation (27).

And S13, determining the nature and the boundary of the integrity countermeasure information. In the examples of the present applicationIn the vehicle control system, the positions of the countermeasure information and the control amount are regarded as equivalent, that is, the input matrices of the countermeasure information and the control amount are identical. The prior information of the countermeasure information is not preset in the boundary, the countermeasure information has any characteristics, is infinitely possible to simulate the Worst case (Worst case) which the vehicle may encounter in the following scene, and is norm-bounded countermeasure information, and the boundary of any moment of the countermeasure information is set as a _adv ∈[-3,3]m/s ² 。

And S2, adopting a linear state feedback control law in the following control of the self vehicle, and decoupling the calculation of the vehicle state reachable set into the calculation of the vehicle difference reachable set and the determination of the vehicle reference track variable.

And S21, establishing a vehicle reference track variable in a vehicle following scene. As shown in fig. 2, it is assumed that there is a reference trajectory of a virtual tracked leading vehicle as a tracking target of the controlled vehicle, the initial state quantity of the reference trajectory is consistent with the vehicle state quantity at the current time, and each state quantity of the reference trajectory is continuously updated iteratively as time changes, as shown in the following equation (28).

Wherein x is _ref As a reference trajectory state vector for tracking, its initial state is kept consistent with the current vehicle state, i.e. x _ref (0) = x (0), known amount; u. of _ref Is a reference trajectory control quantity for tracking.

According to the iterative update rule of the reference track state quantity, the reference track state quantity at any subsequent time can be calculated from the current time, and the iterative relationship abstracted by the equation (8) can be specifically calculated by the following equation (29) in the embodiment of the application.

The matrix a and the matrix B represent a (3 × 3) system matrix and a (3 × 1) input matrix in the expression (28), respectively, and it is known that the reference trajectory state quantity at any time is determined only by all the previous reference trajectory control quantities.

It should be noted that, in the embodiments of the present application, the reference track may be stripped from the state reachable set, or the center of the shadow area in fig. 2 is translated to a coordinate axis, so as to obtain a differential reachable set, where the central vector is a zero vector, and under the action of the classical linear state feedback control law, the differential reachable set and the reference track are decoupled, that is, no matter how the reference track is selected, the differential reachable set is not affected. By designing a virtual track as a reference track, a controlled object tracks the reference track according to a linear feedback control law, as shown in formula (9), and points on the curve in fig. 2 form a central vector of a state reachable set described by Zontope.

And S22, constructing a static linear state feedback control law based on the linear quadratic regulator, and converting the calculation of the vehicle state reachable set of the controlled vehicle into the calculation of the vehicle difference reachable set.

For the reachability analysis based on the static feedback control, the feedback matrix is calculated by adopting a Linear Quadratic Regulator (LQR) method. Before calculating the feedback matrix of the LQR method, a weight matrix regarding the optimization target of the LQR method is first determined, as shown in the following equation (30) (31).

Q＝diag(0.5,0.2,0.2),R＝0.1 (30)

K _lqr ＝lqr(A,B,Q,R)＝[-2.2361 -3.6329 -1.5039] ^T (31)

The weight matrix Q is used for constructing the deviation cost of the actual state and the target state of the vehicle, the weight matrix R is used for constructing the cost of the control input quantity of the vehicle, and the values of the weight matrix Q and the weight matrix R are from common comprehensive consideration on the consideration of the tracking performance and the economic performance of the vehicle; diag denotes a diagonal matrix; LQR is the function for solving the Riccati equation in the LQR method, and can be solved by analytical calculation and then numerical solution or by the corresponding function in Matlab.

Therefore, the linear feedback control law based on the LQR method can be expressed as the following expression (32).

u(k)＝u _ref (k)+K _lqr [x(k)-x _ref (k)] (32)

Wherein, K _lqr The linear state feedback matrix is obtained from equation (31).

And calculating the vehicle difference state quantity as the deviation quantity of the vehicle actual state quantity and the reference track state quantity by combining the vehicle actual state quantity in the following process, and giving an iterative updating rule of the vehicle difference state quantity with time similar to the formula (29), as shown in the following formulas (33) and (34).

x _d (k)＝x(k)-x _ref (k) (33)

According to the iterative update rule of the vehicle differential state quantity, the vehicle differential state quantity at any subsequent time can be calculated from the current time, and the iterative relationship abstracted by the formula (12) can be calculated through the iterative calculation process about the reference trajectory state quantity similar to the formula (29) in the embodiment of the application, and the description is omitted here.

And S3, describing a vehicle difference reachable set under the vehicle following scene by adopting a Zontope set, and performing iterative computation.

And S31, mathematically describing the initial difference reachable and confrontation information sets of the vehicles in the scene of the vehicles by using a Zontope set.

Referring to equation (26), the vehicle differential reachable set in the following scene at any time can be expressed as shown in equation (35) below.

x _d (k)＝[Δs Δv Δa] ^T (35)

Wherein Δ s is a difference between the actual position of the vehicle and the reference position, Δ v is a difference between the actual speed of the vehicle and the reference speed, and Δ a is a difference between the actual acceleration of the vehicle and the reference acceleration.

Considering that the sensing and positioning system carried by the controlled vehicle is not ideal, random errors may exist, and the observation error of each element of the vehicle state is shown as the following formula (36).

|x _d (k)|≤[Δs _err Δv _err Δa _err ] ^T (36)

Wherein, Δ s _err To representUpper limit of position observation error (m), Δ v _err Represents the upper limit of the speed observation error (m/s), Δ a _err Represents the upper limit (m/s) of the observation error of the acceleration ² ) In the present embodiment, the upper limit values are uniformly set to 0.5.

Therefore, the initial difference reachable set that accounts for the state observation error can be mathematically described by the Zonotope set, as shown in equation (37) below.

S ^d ＝(0 _3×1 ,<0.5I _3×3 >) (37)

Wherein S is ^d The method is an initial difference reachable set under a Zontope description method, wherein a central vector is a zero vector, and the dimension of the initial difference reachable set is consistent with the vehicle state under a vehicle following scene; I.C. A _3×3 A 3 rd order identity matrix is represented, each column of which represents a respective generated vector of the initial difference reachable set.

Further, according to the modeling and boundary setting of the countermeasure information in the embodiment S13 of the present application, the infinite norm bounded countermeasure information can also be described as a zontoppe set, as shown in the following equation (38).

D _w ＝(0 _1×1 ,<3I _1×1 >) (38)

Wherein D is _w The countermeasure information of the vehicle is a bounded set, and the central vector of the countermeasure information is a numerical value 0; i is _1×1 The unit matrix of order 1 is represented, i.e. the value 1.

And S32, iteratively calculating a vehicle difference reachable set at each moment under the vehicle following scene. According to the iteration rule described by the equation (11) and the mathematical property of the zontoppe set, the vehicle differential reachable set in the scene of the following vehicle is calculated step by step based on the differential reachable set calculation rule at the next time given by the equation (17), as shown in the following equation (39).

Wherein the content of the first and second substances,

l is a vehicle difference reachable set at each moment; the matrix A, the matrix B and the matrix C are each a system matrix and an input matrix corresponding to the formula (25)Are all known amounts; matrix K _lqr Is a known static feedback matrix obtained based on the LQR method.

Therefore, after the initial difference reachable set and the countermeasure information set of the vehicle in the vehicle following scene are determined, the vehicle difference reachable set described by zontope at each time in the future can be calculated iteratively, and a computing platform of the remote control center can perform numerical calculation of the reachable set by using computing software (such as Matlab). From the current moment of the following vehicle scene, a 10-step difference reachable set is calculated backwards as shown in formula (39), and a plurality of two-dimensional projection graphs can be drawn on the boundary of the difference reachable set at each future moment in a high-dimensional space by adopting auxiliary tool packages such as MPT3, CORA2018 and the like in a calculation software environment (such as Matlab) of a remote control center, as shown in FIG. 8, the evolution characteristic of the controlled own vehicle difference reachable set in the following vehicle scene is presented more intuitively.

And S4, in a car following scene, optimizing the linear state feedback control law and solving a corresponding feedback matrix sequence according to the feedback control law obtained by the calibration LQR method and based on the vehicle difference reachable expression.

And S41, regarding the feedback matrix as variable in the linear feedback control law of the following scene, and introducing a dynamic feedback matrix sequence variable as shown in the following formula (40).

K (K) represents a feedback matrix variable of the moment K and is to be optimized and solved; in the embodiment of the application, there are N feedback matrix variables, which are K (0), K (1), L, and K (N-1), respectively, and the feedback matrix variable K (K) at any time contains 3 unknown element variables a _1k ,a _2k ,a _3k And thus the total number of element variables is 3N.

And S42, constructing an optimization problem about the space size and the shape of the difference reachable set according to the target static feedback control law in the scene of vehicle following. And (4) taking the feedback matrix as a variable, calculating the difference reachable set of the vehicle under the scene of the vehicle step by step again, wherein the calculation method is consistent with that of the static feedback control law, and the difference reachable set containing the matrix variable is shown as the following formula (41).

l is a vehicle difference reachable set at each moment; k (0), K (1) and L are variables of each feedback matrix, and the other matrixes are known and keep the values consistent with the formula (39).

And (3) constructing an optimization problem for a standard static feedback control law so as to realize size reduction and shape remodeling of the difference reachable set and ensure that the reference trajectory control quantity limit is not excessively contracted, as shown in the following formula.

Wherein, K (·) represents feedback matrix variables K (0), K (1), L, K (N-1), which are optimization variables;

a weight matrix for each dimension for reshaping the set shape;

a vector is generated for the jth of time instant k.

In the embodiment of the present application, the value of the weight matrix in the optimization problem is based on the extreme difference of the constraint set in each dimension in the following scene, as shown in fig. 7, given the constraint in the following scene, the following formula (44) represents the following distance deviation constraint, the following speed deviation constraint, and the following acceleration limit constraint of the host vehicle, respectively.

Where s denotes a vehicle position (m), v denotes a vehicle speed (m/s), and a denotes a vehicle acceleration (m/s) ² )；s _p Indicating the position (m), v of the leading vehicle _p Represents the front vehicle speed (m/s); d is a radical of _des Represents a desired following distance (m), which is set to a constant value of 10m in the embodiment of the present application; d _safe Represents an upper limit (m) of the following distance deviation, and is set to be a fixed value of 1m in the embodiment of the application; Δ v _safe The upper limit (m/s) of the following speed deviation amount is set as a fixed value of 0.5m/s in the embodiment of the application; a is _max Shows the upper limit of the acceleration (m/s) of the car following ² ) In the present embodiment, the value is set to 5m/s ² 。

The value of the weight matrix in the optimization problem can be determined according to equation (21.5), as shown in equation (45).

ω _k ＝[1/2d _safe 1/2Δv _safe 1/2a _max ] ^T ＝[0.5 1 0.1] ^T (45)

And S43, solving the optimized dynamic feedback matrix sequence in the car following scene, and updating the optimized control law. In a computing software environment (such as Matlab) of a remote control center, an auxiliary tool (such as YALMIP) for constructing and solving an optimization problem is adopted ^[5] ) Selecting a proper optimization algorithm (such as Newton method, interior point method and the like), and solving the optimization problem to obtain an optimal feedback matrix sequence K ^* (0),K ^* (1),L,K ^* (N-1), and updating the optimized control law as shown in the following formula (46).

u(k)＝u _ref (k)+K ^* (k)[x(k)-x _ref (k)] (46)

Wherein, K ^* (k) And the optimal feedback matrix variable representing the time k is a matrix value.

And S5, carrying out numerical calculation on the difference reachable set after optimization of the vehicle at each future moment in the scene of the following vehicle. Optimizing a feedback matrix sequence K ^* (0),K ^* (1),L,K ^* (N-1) is substituted into formula (41), the value of the vehicle differential reachable set optimized under the scene of the vehicle can be calculated, and the reachable set at any moment can be calculated in a remote control centerIn the software environment (e.g., matlab), an auxiliary tool kit such as MPT3 and CORA2018 may be used for visual expression, and in the embodiment of the present application, the reachable sets before and after optimization may be simultaneously drawn into a three-dimensional perspective view, as shown in fig. 9, so as to highlight the optimization effect of the reachable sets of vehicles in the scene following the vehicle.

And S6, coupling the vehicle reference track in the following vehicle scene with the optimized difference reachable set, and calculating to obtain the state reachable set containing the reference track variable after the vehicle is optimized at each moment in the future. In the following scenario of the embodiment of the present application, the state reachable set of the host vehicle is composed of the reference trajectory state quantity and the difference reachable set, and as shown in fig. 2, the reference trajectory state quantity and the difference reachable set are re-coupled, as shown in the following equation (47).

Wherein R is _k A reachable set of vehicle states at time k; x is a radical of a fluorine atom _ref (k) Is the reference track state quantity at the time k;

the difference reachable set optimized for time k.

The reference track state quantity is a vector quantity, the difference reachable set is a known Zontope set, and the reachable set of the vehicle state at each future time can be explicitly calculated and expressed according to the Zontope set characteristics, as shown in the following formula (48).

Wherein the content of the first and second substances,

l is the vehicle difference reachable set after optimization at each moment; k ^* (0),K ^* (1) L is a known optimal feedback matrix sequence; x is the number of _ref (0),x _ref (1) And L is the state quantity of the reference track at each moment and is a vector variable.

So far, according to the embodiment of the application, a vehicle state reachable set in a vehicle following scene is obtained and presented in a zontope set form, wherein only a reference track variable is included as a function of a reference track. Actually, the reference trajectory state quantity at the current time is determined as the current vehicle state observed value in S21, and it is known from equation (29) that the reference trajectory state quantity at any time is determined only by all the previous reference trajectory control quantities. Therefore, the reachable set of the vehicle state under the scene of following the vehicle is also the control quantity sequence u of the reference track _ref (0),u _ref (1) And L. To realize the control safety of vehicles containing one kind of integrity countermeasure information in the subsequent vehicle following scene, only the reference track needs to be reasonably planned, and the reference track control quantity sequence u is output _ref (0),u _ref (1) And L, enabling the reachable set of the vehicle state at each moment in the future to meet the constraint. In the embodiment of the application, the method of the embodiment of the application is used for quantitatively describing the influence range of the countermeasure information on the vehicle state in the vehicle following scene, and the influence range corresponds to the vehicle reference track one by one, so that basic guarantee is provided for realizing the control safety of the vehicle in the vehicle following scene.

According to the following control method of the vehicle under the countermeasure information, a control system model of the vehicle is established through the countermeasure information of the vehicle, the calculation of the vehicle state reachable set is decoupled into the calculation of the vehicle difference reachable set and the determination of the vehicle reference track variable through combining the linear state feedback control law, so that the mathematical expression of the vehicle difference reachable set is obtained in an iterative mode, the method for optimizing the dynamic feedback matrix sequence is provided, the space size and the shape of the calculated reachable set are optimized, the difference reachable set can be reduced and remolded, the control quantity limit is not excessively tightened, the balance relation between the existing feedback matrix and the control quantity limit is relieved to a certain extent, and basic guarantee is provided for the control safety of the vehicle under the following scene. Therefore, the problems that the reachable set calculation method in the related technology is low in calculation efficiency, over-approximate calculation is performed, optimization of the reachable set is not involved and the like are solved.

Next, a following control apparatus of a vehicle under countermeasure information according to an embodiment of the present application will be described with reference to the drawings.

Fig. 10 is a block diagram schematically illustrating a following control apparatus of a vehicle under countermeasure information according to an embodiment of the present application.

As shown in fig. 10, the following control device 10 of the vehicle under the countermeasure information includes: an acquisition module 100, a processing module 200, a first calculation module 300, a second calculation module 400, and a control module 500.

The obtaining module 100 is configured to obtain preset countermeasure information of a vehicle; the processing module 200 is configured to establish a control system model of the vehicle according to the preset reactance information, and obtain a reference trajectory state quantity and an initial difference reachable set of the vehicle at each preset time after the current time by using a preset linear state feedback control law decoupling control system model; the first calculating module 300 is configured to iteratively calculate an initial difference reachable set at each preset time to obtain a difference reachable set expression of the vehicle, optimize a preset linear state feedback control law based on the difference reachable set expression, and solve the optimized preset linear state feedback control law to obtain an optimal feedback matrix sequence; the second calculation module 400 is configured to iteratively calculate an initial difference reachable set at each preset time based on the optimal feedback matrix sequence and the optimized preset linear state feedback control law to obtain a numerical vector at each preset time; the control module 500 is configured to couple the numerical vector at each preset time and the reference trajectory state quantity to obtain a final difference reachable set, predict a vehicle following trajectory of the vehicle at a next time based on the final difference reachable set, and control the vehicle to travel along the vehicle following trajectory.

In one embodiment of the present application, the processing module 200 is further configured to use the preset reactance information as an input to a preset continuous linear system of the vehicle; abstract modeling and analyzing longitudinal dynamics and transverse dynamics of the vehicle based on a preset linear system to obtain a dynamic model of the vehicle; and discretizing the discretization dynamic model to obtain a discretization system model, and determining the property and the boundary of preset resistance information to obtain a control system model.

In one embodiment of the present application, the processing module 200 is further configured to obtain a reference trajectory control quantity and an actual state quantity of the vehicle; inputting the reference track control quantity into a control system model for iterative updating to obtain a reference track state quantity of the vehicle at each preset moment; and calculating the differential state quantity of the vehicle according to the offset of the reference track state quantity, iteratively updating the actual state quantity and the differential state quantity according to the vehicle by using a preset linear state feedback control law to obtain the differential state of the vehicle at each preset moment, and establishing an initial differential reachable set based on the differential state of the vehicle at each preset moment.

In one embodiment of the present application, the first computing module 300 is further configured to mathematically describe the initial difference reachability and countermeasure information sets using a zontope set, and determine an iteration rule and mathematical properties of the zontope set; performing iterative computation on the difference reachable set at the known moment according to the iteration rule and the mathematical property of the Zontope set to obtain the difference reachable set at the next moment; and determining a generated vector based on the difference reachable set of the next moment obtained by iterative computation, and obtaining the expression of the difference reachable set of the vehicle according to the generated vector.

In one embodiment of the present application, the first computation module 300 is further configured to iteratively compute a dynamic feedback matrix sequence variable based on the differential reachable set expression; optimizing a preset linear state feedback control law according to the dynamic feedback matrix sequence variables to obtain the optimized preset linear state feedback control law; and constructing an optimization problem of the space size and the shape of the difference reachable set according to a preset standard static feedback control law, and solving the optimization problem based on a preset linear state feedback control law to obtain an optimal feedback matrix sequence.

It should be noted that the foregoing explanation of the embodiment of the method for controlling vehicle following under countermeasure information is also applicable to the vehicle following control device for vehicle following under countermeasure information of this embodiment, and will not be described again here.

According to the following control device of the vehicle under the countermeasure information provided by the embodiment of the application, a control system model of the vehicle is established through the countermeasure information of the vehicle, the calculation of the vehicle state reachable set is decoupled into the calculation of the vehicle difference reachable set and the determination of the vehicle reference track variable through combining a linear state feedback control law, so that the mathematical expression of the vehicle difference reachable set is obtained in an iterative mode, a method for optimizing a dynamic feedback matrix sequence is provided, the space size and the shape of the calculated reachable set are optimized, the difference reachable set can be reduced and remolded, the control quantity limit is not excessively tightened, the balance relation between the existing feedback matrix and the control quantity limit is relieved to a certain extent, and basic guarantee is provided for the control safety of the vehicle under the following scene. Therefore, the problems that the reachable set calculation method in the related technology is low in calculation efficiency, over-approximate calculation is performed, optimization of the reachable set is not involved and the like are solved.

Fig. 11 is a schematic structural diagram of a vehicle according to an embodiment of the present application. The vehicle may include:

a memory 1101, a processor 1102, and a computer program stored on the memory 1101 and executable on the processor 1102.

The processor 1102, when executing the program, implements the following control method of the vehicle under the countermeasure information provided in the above-described embodiment.

Further, the vehicle further includes:

a communication interface 1103 for communicating between the memory 1101 and the processor 1102.

A memory 1101 for storing computer programs that are executable on the processor 1102.

The Memory 1101 may comprise a high-speed RAM (Random Access Memory) Memory, and may also include a non-volatile Memory, such as at least one disk Memory.

If the memory 1101, the processor 1102 and the communication interface 1103 are implemented independently, the communication interface 1103, the memory 1101 and the processor 1102 may be connected to each other through a bus and perform communication with each other. The bus may be an ISA (Industry Standard Architecture) bus, a PCI (Peripheral Component interconnect) bus, an EISA (Extended Industry Standard Architecture) bus, or the like. The bus may be divided into an address bus, a data bus, a control bus, etc. For ease of illustration, only one thick line is shown in FIG. 11, but that does not indicate only one bus or one type of bus.

Optionally, in a specific implementation, if the memory 1101, the processor 1102 and the communication interface 1103 are integrated on one chip, the memory 1101, the processor 1102 and the communication interface 1103 may complete communication with each other through an internal interface.

The processor 1102 may be a Central Processing Unit (CPU), an Application Specific Integrated Circuit (ASIC), or one or more Integrated circuits configured to implement embodiments of the present Application.

An embodiment of the present application also provides a computer-readable storage medium on which a computer program is stored, which, when executed by a processor, implements the following control method of a vehicle under countermeasure information as above.

In the description of the present specification, reference to the description of "one embodiment," "some embodiments," "an example," "a specific example," or "some examples" or the like means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present application. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or N embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.

Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present application, "N" means at least two, e.g., two, three, etc., unless specifically limited otherwise.

Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more N executable instructions for implementing steps of a custom logic function or process, and alternate implementations are included within the scope of the preferred embodiment of the present application in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of implementing the embodiments of the present application.

It should be understood that portions of the present application may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods may be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. If implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a programmable gate array, a field programmable gate array, or the like.

It will be understood by those skilled in the art that all or part of the steps carried out in the method of implementing the above embodiments may be implemented by hardware related to instructions of a program, which may be stored in a computer readable storage medium, and the program, when executed, includes one or a combination of the steps of the method embodiments.

Claims

1. A car following control method of a vehicle under countermeasure information, characterized by comprising the steps of:

acquiring preset countermeasure information of a vehicle;

establishing a control system model of the vehicle according to the preset reactance information, and decoupling the control system model by adopting a preset linear state feedback control law to obtain a reference track state quantity and an initial difference reachable set of the vehicle at each preset moment after the current moment;

iteratively calculating an initial difference reachable set at each preset time to obtain a difference reachable set expression of the vehicle, optimizing the preset linear state feedback control law based on the difference reachable set expression, and solving to obtain an optimal feedback matrix sequence based on the optimized preset linear state feedback control law;

iteratively calculating an initial difference reachable set of each preset moment based on the optimal feedback matrix sequence and the optimized preset linear state feedback control law to obtain a numerical vector of each preset moment;

and coupling the numerical vector and the reference track state quantity at each preset moment to obtain a final difference reachable set, predicting a following track of the vehicle at the next moment based on the final difference reachable set, and controlling the vehicle to run along the following track.

2. The method of claim 1, wherein said modeling a control system of said vehicle based on said predetermined reactance information comprises:

taking the preset reactance information as the input of a preset continuous linear system of the vehicle;

carrying out abstract modeling and analysis on longitudinal dynamics and transverse dynamics of the vehicle based on the preset linear system to obtain a dynamic model of the vehicle;

discretizing the dynamic model to obtain a discretization system model, and determining the property and the boundary of the preset reactance information to obtain the control system model.

3. The method of claim 1, wherein the decoupling the control system model using a preset linear state feedback control law to obtain a reference trajectory state quantity and an initial difference reachable set of the vehicle at each preset time after the current time comprises:

acquiring a reference track control quantity and an actual state quantity of the vehicle;

inputting the reference track control quantity into the control system model for iterative update to obtain a reference track state quantity of the vehicle at each preset moment;

and calculating the differential state quantity of the vehicle according to the offset of the reference track state quantity, performing iterative update on the actual state quantity and the differential state quantity according to the vehicle by using the preset linear state feedback control law to obtain the differential state of the vehicle at each preset moment, and establishing the initial differential reachable set based on the differential state of the vehicle at each preset moment.

4. The method of claim 1, wherein iteratively calculating the initial difference reachable set at each preset time to obtain the difference reachable set expression of the vehicle comprises:

carrying out mathematical description on the initial difference reachable and antagonistic information sets by adopting a Zontope set, and determining an iteration rule and mathematical properties of the Zontope set;

performing iterative computation on the difference reachable set at the known moment according to the iteration rule and the mathematical property of the Zontope set to obtain the difference reachable set at the next moment;

and determining a generated vector based on a difference reachable set at the next moment obtained by iterative computation, and obtaining a difference reachable set expression of the vehicle according to the generated vector.

5. The method according to claim 1, wherein the optimizing the preset linear state feedback control law based on the differential reachable set expression and solving to obtain an optimal feedback matrix sequence based on the optimized preset linear state feedback control law comprises:

iteratively calculating a dynamic feedback matrix sequence variable based on the difference reachable set expression;

optimizing the preset linear state feedback control law according to the dynamic feedback matrix sequence variable to obtain the optimized preset linear state feedback control law;

and constructing an optimization problem of the space size and the shape of a difference reachable set according to a preset standard static feedback control law, and solving the optimization problem based on the preset linear state feedback control law to obtain the optimal feedback matrix sequence.

6. A following control apparatus of a vehicle under countermeasure information, characterized by comprising:

the acquisition module is used for acquiring preset countermeasure information of the vehicle;

the processing module is used for establishing a control system model of the vehicle according to the preset reactance information and decoupling the control system model by adopting a preset linear state feedback control law to obtain a reference track state quantity and an initial difference reachable set of the vehicle at each preset moment after the current moment;

the first calculation module is used for iteratively calculating an initial difference reachable set at each preset moment to obtain a difference reachable set expression of the vehicle, optimizing the preset linear state feedback control law based on the difference reachable set expression, and solving to obtain an optimal feedback matrix sequence based on the optimized preset linear state feedback control law;

the second calculation module is used for iteratively calculating an initial difference reachable set of each preset moment based on the optimal feedback matrix sequence and the optimized preset linear state feedback control law to obtain a numerical vector of each preset moment;

and the control module is used for coupling the numerical vector and the reference track state quantity at each preset moment to obtain a final difference reachable set, predicting a following track of the vehicle at the next moment based on the final difference reachable set, and controlling the vehicle to run along the following track.

7. The apparatus of claim 6, wherein the processing module is further configured to:

discretizing the dynamic model to obtain a discretized system model, and determining the property and the boundary of the preset resistance information to obtain the control system model.

8. The apparatus of claim 6, wherein the first computing module is further configured to:

carrying out iterative computation on the difference reachable set at the known moment according to the iteration rule and the mathematical property of the Zontope set to obtain the difference reachable set at the next moment;

and determining a generated vector based on the difference reachable set of the next moment obtained by iterative computation, and obtaining the expression of the difference reachable set of the vehicle according to the generated vector.

9. A vehicle, characterized by comprising: a memory, a processor and a computer program stored on the memory and executable on the processor, the processor executing the program to implement the following control method of a vehicle under countermeasure information according to any one of claims 1 to 5.

10. A computer-readable storage medium on which a computer program is stored, the program being executed by a processor for implementing the following control method of a vehicle under countermeasure information according to any one of claims 1 to 5.