CN112034859B - Self-adaptive dynamic planning method of anti-interference CACC system - Google Patents

Self-adaptive dynamic planning method of anti-interference CACC system Download PDF

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CN112034859B
CN112034859B CN202010959308.4A CN202010959308A CN112034859B CN 112034859 B CN112034859 B CN 112034859B CN 202010959308 A CN202010959308 A CN 202010959308A CN 112034859 B CN112034859 B CN 112034859B
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matrix
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CN112034859A (en
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高振宇
安会爽
郭戈
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Northeastern University Qinhuangdao Branch
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0223—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving speed control of the vehicle
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0214—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory in accordance with safety or protection criteria, e.g. avoiding hazardous areas
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0221—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving a learning process
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0276—Control of position or course in two dimensions specially adapted to land vehicles using signals provided by a source external to the vehicle
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0287—Control of position or course in two dimensions specially adapted to land vehicles involving a plurality of land vehicles, e.g. fleet or convoy travelling
    • G05D1/0291—Fleet control
    • G05D1/0295—Fleet control by at least one leading vehicle of the fleet

Abstract

The invention provides an anti-interference self-adaptive dynamic programming method of a CACC system, and relates to the technical field of heterogeneous fleet control. The invention solves the motorcade stability problem under the condition of simultaneous delay of an actuator, external interference and front vehicle interference by constructing a model and providing the ADP motorcade cooperative control method based on data driving, and the method can enable the motorcade to quickly reach a stable state. In the analysis of the stability of the vehicle, the stability of the vehicle is proved by analyzing the magnitude of the cost function updated by the controller. The cost function is bounded and is smaller than a minimum value, which proves that the state of the vehicle and the control input reach a stable state.

Description

Self-adaptive dynamic planning method of anti-interference CACC system
Technical Field
The invention relates to the technical field of heterogeneous fleet control, in particular to an adaptive dynamic planning method for an anti-interference CACC system.
Background
In recent years, research on heterogeneous vehicle fleets is still limited, and a control method based on data driving is rarely applied to vehicle fleet Coordinated Adaptive Cruise Control (CACC). With the rapid development of the technology in the field of artificial intelligence, jiang et al y.vehicular and z. -p.j., comprehensive adaptive optimal control for continuous-time linear systems with complex un-known dynamics, "automotive, vol.48, No.10, pp.2699-2704,2012. and y.j.j.z. -p.j., road adaptive dynamic programming and feedback stabilization of non-linear systems," IEEE trans.neural net.leirn.25, vol.25, No.5, pp.882-893, may2014. In Gao et al work, Gao W, Jiang ZP, Ozbay K.Data-driven adaptive optimal control of connected vehicles.IEEE Trans inner Transp Syst.2017; 18(5):1122 & 1133. and K.J.Malakorn and B.park, "Assessment of mobility, energy, and environmental impacts of Intelligent-based adaptive cruise control and internal traffic control," in Proc.IEEE. Symp.Sustain.Syhnol, May2010, pp.1-6. ADP are applied to the adaptive optimal control of the data-driven interconnected vehicle. In the aspect of cooperative adaptive fleet control, communication interference problems and fleet stability control in an interference environment currently face challenges.
In the above studies, input skew due to engine process delay was not considered in the controller design process, which greatly limited its application in practical heterogeneous fleet control. In addition, interference in the networked vehicle system comes from different aspects, such as unpredictable acceleration or deceleration of the front vehicle, signal interference in the communication process and the like.
Due to the second-order fleet model adopted by the controller design, the second-order fleet model cannot well capture dynamic characteristics inside the vehicle, and various interference problems in the travelling process of the fleet need to be considered. Furthermore, it is also important to analyze and verify the stability of each vehicle, i.e. to ensure that the inter-vehicle distance between adjacent vehicles does not continuously enlarge from lead vehicle to the last vehicle.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides an adaptive dynamic planning method of an anti-interference CACC system, which constructs a three-order dynamics model of a fleet covering various interference factors, realizes cooperative control of the fleet by reasonable inter-vehicle distance, ensures that vehicles run quickly and stably, and strictly deduces and proves the stability of each vehicle in the fleet.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
an adaptive dynamic planning method of an anti-interference CACC system comprises the following steps:
step 1, constructing a fixed time interval strategy according to the dynamic performance of a vehicle, and establishing a longitudinal dynamic model of the vehicle by adopting a one-way communication structure;
the vehicle longitudinal dynamics model does not contain a lead vehicle, and the inter-vehicle distance error of the ith vehicle is defined to be delta p i (t) having:
Δp i (t)＝p i-1 (t)-p i (t)-d s -L,i＝1,2,...,n
wherein d is s ＝h i v i (t)+r i Is the desired inter-vehicle distance, h i Is a constant headway, v i (t) is the speed of the ith vehicle at time t, r i Fixed inter-vehicle distance, p i (t) is the position of the ith vehicle at time t, L is the vehicle length;
the dynamical model of the ith vehicle is the following nonlinear differential equation:
Figure BDA0002679850150000021
wherein, Δ v i (t) is the speed error of the ith vehicle at time t, a i (t) is the acceleration of the ith vehicle at time t, c i (t) is the feedback linearization control law, h i Constant headway is constant, f i (v i ,a i ) Is a non-linear dynamic model of the vehicle,
Figure BDA0002679850150000022
is a constant;
for a lead car, since it has no front car, its kinematic model is defined as follows:
Figure BDA0002679850150000023
Figure BDA0002679850150000024
where σ is the specific mass of air, τ i Is the mechanical time constant, A i ,c di ,d mi And m i The cross-sectional area, the drag coefficient, the mechanical resistance and the mass of the ith vehicle are respectively;
linearizing the model to obtain a feedback linearization control law as follows:
Figure BDA0002679850150000025
the following linearized models were obtained:
Figure BDA0002679850150000026
wherein u is i (t) is an additional control input signal;
adding disturbance xi to the linearized model due to communication failure or external disturbance in the networking environment i (t); the linearization model after adding the disturbance is:
Figure BDA0002679850150000031
wherein
Figure BDA0002679850150000032
ξ i (t) and
Figure BDA0002679850150000033
are respectively disturbance xi i (t) a lower bound and an upper bound;
step 2, setting the whole fleet to be composed of 1 leading vehicle and n following vehicles, respectively constructing controller models of the leading vehicle and the following vehicles, and providing a controller optimization algorithm based on data driving;
the controller model of the lead vehicle is as follows:
u 0 (t)＝-K 0 x 0 (t)
wherein x 0 (t)＝[p 0 (t) v 0 (t) a 0 (t)] T ，p 0 (t)、v 0 (t) and a 0 (t) the position, speed and acceleration of the lead vehicle at the moment t, and the feedback control rate K of the lead vehicle 0 ＝[k 01 k 02 k 03 ]Wherein k is 01 ，k 02 ，k 03 Respectively, the position, the speed and the acceleration of the lead vehicle.
The vehicle-following kinetic model is:
Figure BDA0002679850150000034
wherein the content of the first and second substances,
Figure BDA0002679850150000035
i＝1,2,…,n，x i (t)＝[Δp i (t) Δv i (t) a i (t)] T ；Δp i (t) is the position error of the ith vehicle from the target position at time t, Δ v i (t) is the speed error between the ith vehicle and the preceding vehicle at time t, and the controller u i (t)＝-K i x i (t)，K i ＝[k i1 k i1 k i2 ]The feedback control laws respectively follow the position, speed and acceleration of the vehicle. The controller after the unfolding is obtained as follows:
u i (t)＝-k i1 Δp i (t)-k i2 Δv i (t)-k i3 a i (t)
the vehicle-following dynamics model is rewritten as:
Figure BDA0002679850150000036
wherein the content of the first and second substances,
Figure BDA0002679850150000037
j＝0,1,…,n，ω i (t)＝D i x i-1 (t)+I i ξ i (t)，A ij is a coefficient matrix of the state inputs of i cars after iteration j times, B i Is a coefficient matrix of control inputs for i cars, D i Is a coefficient matrix of the status inputs of the i-1 vehicle,
Figure BDA0002679850150000038
is the control gain for i cars after j iterations.
The controller u i (t) the optimization algorithm comprises the steps of:
step S1: selecting a minimum loss function according to a control target:
Figure BDA0002679850150000039
wherein Q is blockdiag (Q) 1 ,Q 2 ,…,Q n )，
Figure BDA00026798501500000310
R＝blockdiag(R 1 ,R 2 ,…,R n ),
Figure BDA00026798501500000311
Figure BDA0002679850150000041
Is the set of states at time t of all vehicles, u ═ u 1 ,u 2 ,…,u n ] T Is the set of control inputs of all vehicles at the time t, the control gain of all vehicles is K * ＝R -1 B T P * Wherein, P * Solved by algebraic Riccati equation.
Step S2: obtaining the iteration value of the feedback gain of the step j +1 of the ith vehicle according to the Riccati equation
Figure BDA0002679850150000042
Wherein
Figure BDA0002679850150000043
The intermediate value of step j of the ith vehicle;
step S3: since there is no way to predict the parameter matrix A of the vehicles in the fleet i And B i Then, the solution is solved by the following equation, i.e., [ t, t + δ t [ ]]The difference in time is then the minimum loss function:
Figure BDA0002679850150000044
where δ is the signal sample interval time.
According to the kronecker product, and
δ a ＝[vecv(a(t 1 ))-vecv(a(t 0 )),…,vecv(a(t s ))-vecv(a(t s-1 ))] T ,
Figure BDA0002679850150000045
the formula is simplified to obtain:
Figure BDA0002679850150000046
Figure BDA0002679850150000047
Figure BDA0002679850150000048
wherein the content of the first and second substances,
Figure BDA0002679850150000049
is a process matrix and satisfies the column full rank,
Figure BDA00026798501500000410
in the form of a matrix of processes,
Figure BDA00026798501500000411
is a process variable matrix;
step 3, obtaining a data-driven CACC control method according to a data-driven-based controller optimization algorithm;
step 3.1: selecting an initial controller gain K for a follower vehicle 0 And a desired threshold σ > 0;
step 3.2: the initial controller model inputs u (t) ═ K including interference information 0 x (t) + e (t) at time intervals of [ t [, ] 0 ,t s ]；
Step 3.3: calculating a process variable
Figure BDA0002679850150000051
Satisfy the requirements of
Figure BDA0002679850150000052
Let j ← 0;
step 3.4: p pair by using the formula in step S3 (j) ，K (j+1) Solving is carried out;
step 3.5: and j ← j +1, up to | P (j) -P (j-1) |＜σ；
Step 3.6: updating the controller model so that u (t) is equal to-K (j) x(t)；
Step 3.7: returning the updating result of the controller u (t);
when in use
Figure BDA0002679850150000053
When the algorithm converges, i.e. it is
Figure BDA0002679850150000054
And
Figure BDA0002679850150000055
respectively converge to the optimum intermediate value P * And an optimal feedback control gain K * ；
Step 4, constructing a following vehicle differential equation according to the dynamic performance of the vehicle, and proving the stability of the following vehicle;
step 4.1: firstly, constructing a following vehicle dynamic equation:
Figure BDA0002679850150000056
wherein [ delta ] | is not more than rho is interfered when the vehicle runs, and is obtained according to the steps of 3.1-3.7, and exists
Figure BDA0002679850150000057
Epsilon is more than 0 to obtain the estimated optimal controller of the vehicle
Figure BDA0002679850150000058
Step 4.2: when T is less than or equal to s is less than or equal to T + T,
Figure BDA0002679850150000059
when there is a minimum value epsilon i Time, matrix
Figure BDA00026798501500000510
Is always a Hulviz matrix and finds the constant β i ,λ i Is greater than 0, and satisfies:
Figure BDA00026798501500000511
wherein i is 1,2, …, n;
step 4.3: for the lead car:
Figure BDA00026798501500000512
β 0 ,λ 0 is constant, thus proving that the closed loop system of the vehicle is exponentially stable.
Step 5, constructing a transfer matrix to prove the optimality of the controller;
defining a minimum loss function J according to the minimum loss function proof ⊙ ＝x T (0)P * x (0), obtained in step 3, the state transition matrix phi (tau, t) satisfies that phi (tau, t) is less than or equal to beta e λ(τ-t) ,
Figure BDA00026798501500000514
Definition of
Figure BDA00026798501500000513
Presence of c 1 ,c 2 >0 is a constant number of times, and,
Figure BDA0002679850150000061
wherein
Figure BDA0002679850150000062
Is semi-positive and continuously differentiable, and has an upper limit of
Figure BDA0002679850150000063
Wherein
Figure BDA0002679850150000064
Φ (τ, τ) ═ I, according to the law of the leibuctz integral, we obtain:
Figure BDA0002679850150000065
distributed minimum loss function
Figure BDA0002679850150000066
Satisfy the requirement of
Figure BDA0002679850150000067
Wherein λ is max (Q) is the maximum eigenvalue of the Q matrix, λ min (P) is the minimum eigenvalue of the P matrix, μ is a constant.
Thus, the controller minimum loss function proves to have optimal performance.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in:
the invention provides an adaptive dynamic planning method of an anti-interference CACC system, which is used for constructing a model and providing an ADP fleet cooperative control algorithm based on data driving, solving the problem of fleet stability under the condition that actuator delay, external interference and front vehicle interference exist simultaneously, and enabling a fleet to reach a stable state quickly. In the analysis of the stability of the vehicle, the stability of the vehicle is proved by analyzing the magnitude of the cost function updated by the controller. The cost function is bounded and is smaller than a minimum value through analysis, and the vehicle state and the control input can be proved to reach a stable state.
The invention establishes a third-order linear fleet dynamics model on the basis of a fleet model with a second order adopted by the cooperative braking control of the traditional interconnected vehicles. Compared with a second-order fleet model, the third-order model can better capture dynamic characteristics inside the vehicle. Aiming at the condition that disturbance exists in the heterogeneous fleet system environment, a controller of a leading fleet vehicle and a cooperative controller of a following fleet vehicle are respectively designed, and an ADP self-adaptive cooperative control algorithm based on data driving is designed, so that the problem of fleet stability under the condition that various disturbances exist simultaneously is solved. The invention provides a data-driven fleet cooperative braking control method, which is used for evaluating the convergence of vehicles by using a cost function. The simulation result verifies the effectiveness of the method.
Drawings
Fig. 1 is a flowchart of an adaptive dynamic programming method of an anti-interference CACC system according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a heterogeneous fleet and communication topology used in an embodiment of the present invention;
FIG. 3 is a schematic diagram of an optimization iteration process according to an embodiment of the present invention;
wherein diagrams (a) -P ij Matrix optimization iterative process, graph (b) -optimization iterative process of error feedback gain
FIG. 4 is a schematic diagram of errors between a following vehicle and a preceding vehicle of a straight lane when a lead vehicle is disturbed according to an embodiment of the invention;
wherein, the following vehicle v1 and the preceding vehicle error condition when the vehicle runs on the straight lane, the following vehicle v2 and the preceding vehicle error condition when the vehicle runs on the straight lane, and the following vehicle v3 and the preceding vehicle error condition when the vehicle runs on the straight lane are shown in the graph (a);
FIG. 5 is a schematic diagram of errors between a following vehicle and a preceding vehicle of a straight lane when a lead vehicle is undisturbed according to the embodiment of the invention;
wherein, figure (a) shows the following vehicle v1 and the front vehicle error condition when the vehicle runs on the straight lane; (b) following vehicle v2 versus preceding vehicle error condition while driving in straight lane; (c) following vehicle v3 versus preceding vehicle error while driving in straight lane
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
The heterogeneous fleet model provided by the embodiment comprehensively considers actuator faults and external interference, adopts an ADP algorithm based on data driving, and designs the cooperative controller, so that the convergence of each vehicle in the whole braking process of the fleet can be realized, and the queue stability of the whole fleet can be realized.
An adaptive dynamic planning method for an anti-interference CACC system, as shown in fig. 1, includes the following steps:
step 1, constructing a fixed time interval strategy according to the dynamic performance of a vehicle, and establishing a longitudinal dynamic model of the vehicle by adopting a one-way communication structure;
the vehicle longitudinal dynamics model does not contain a lead vehicle, and the inter-vehicle distance error of the ith vehicle is defined to be delta p i (t) having:
Δp i (t)＝p i-1 (t)-p i (t)-d s -L,i＝1,2,...,n
wherein d is s ＝h i v i (t)+r i Is the desired inter-vehicle distance, h i Is a constant headway, v i (t) is the speed of the ith vehicle at time t, r i Fixed inter-vehicle distance, p i (t) is the position of the ith vehicle at time t, and L is the vehicle length;
the kinetic model of the ith vehicle is the following nonlinear differential equation:
Figure BDA0002679850150000071
wherein, Δ v i (t) is the speed error of the ith vehicle at time t, a i (t) is the acceleration of the ith vehicle at time t, c i (t) is the feedback linearization control law, h i Constant headway is constant, f i (v i ,a i ) Is a non-linear dynamic model of the vehicle,
Figure BDA0002679850150000072
is a constant;
for a lead car, since it has no front car, its kinematic model is defined as follows:
Figure BDA0002679850150000073
Figure BDA0002679850150000074
where σ is the specific mass of air, τ i Is the mechanical time constant, A i ,c di ,d mi And m i The cross-sectional area, drag coefficient, mechanical drag and mass of the ith vehicle respectively;
linearizing the model to obtain a feedback linearization control law as follows:
Figure BDA0002679850150000081
the following linearized models were obtained:
Figure BDA0002679850150000082
wherein u is i (t) adding a control input signal to enable the closed-loop system to meet stable anti-interference performance indexes; with this controller, the following two objectives are achieved: 1) ith vehicle motionMechanical linearization; 2) the system model is simplified by excluding some characteristic parameters in the vehicle dynamics, such as mechanical resistance, mass and air resistance.
Adding disturbance xi to the linearized model due to communication failure or external disturbance in the networking environment i (t); the linearization model after adding the disturbance is:
Figure BDA0002679850150000083
wherein
Figure BDA0002679850150000084
ξ i (t) and
Figure BDA0002679850150000085
are respectively disturbance xi i (t) a lower bound and an upper bound;
step 2, setting the whole fleet to be composed of 1 leading vehicle and n following vehicles, respectively constructing controller models of the leading vehicle and the following vehicles as shown in fig. 2, and providing a controller optimization algorithm based on data driving;
the controller model of the lead vehicle is as follows:
u 0 (t)＝-K 0 x 0 (t)
wherein x 0 (t)＝[p 0 (t) v 0 (t) a 0 (t)] T ，p 0 (t)、v 0 (t) and a 0 (t) is the position, speed and acceleration of the lead vehicle at the moment t, and the feedback control rate K of the lead vehicle 0 ＝[k 01 k 02 k 03 ]Wherein k is 01 ，k 02 ，k 03 Respectively, the position, the speed and the acceleration of the lead vehicle.
The vehicle-following kinetic model is:
Figure BDA0002679850150000086
wherein the content of the first and second substances,
Figure BDA0002679850150000087
i＝1,2,…,n，x i (t)＝[Δp i (t) Δv i (t) a i (t)] T ；Δp i (t) is the position error of the ith vehicle from the target position at time t, Δ v i (t) is the speed error between the ith vehicle and the preceding vehicle at time t, and the controller u i (t)＝-K i x i (t)，K i ＝[k i1 k i1 k i2 ]The feedback control laws respectively follow the position, speed and acceleration of the vehicle. The controller after the unfolding is obtained as follows:
u i (t)＝-k i1 Δp i (t)-k i2 Δv i (t)-k i3 a i (t)
the vehicle-following dynamics model is rewritten as:
Figure BDA0002679850150000091
wherein the content of the first and second substances,
Figure BDA0002679850150000092
j＝0,1,…,n，A ij is a coefficient matrix of the state inputs of i cars after iteration j times, B i Is a coefficient matrix of control inputs for i cars, D i Is a coefficient matrix of the status inputs of the i-1 vehicle,
Figure BDA00026798501500000911
is the control gain for i cars after j iterations.
The controller u i (t) the optimization algorithm comprises the steps of:
step S1: selecting a minimum loss function according to a control target:
Figure BDA0002679850150000093
wherein Q is blockdiag (Q) 1 ,Q 2 ,…,Q n )，
Figure BDA0002679850150000094
R＝blockdiag(R 1 ,R 2 ,…,R n ),
Figure BDA0002679850150000095
Figure BDA0002679850150000096
Is the set of states of all vehicles at time t, u ═ u 1 ,u 2 ,…,u n ] T Is the set of control inputs of all vehicles at the time t, the control gain of all vehicles is K * ＝R -1 B T P * Wherein P is * Solved by algebraic Riccati equation.
Step S2: obtaining the iteration value of the feedback gain of the step j +1 of the ith vehicle according to the Riccati equation
Figure BDA0002679850150000097
Wherein
Figure BDA0002679850150000098
The intermediate value of step j of the ith vehicle;
step S3: since there is no way to predict the parameter matrix A of the vehicles in the fleet i And B i Then, the solution is solved by the following equation, i.e., [ t, t + δ t [ ]]The difference in time is then the minimum loss function:
Figure BDA0002679850150000099
where δ is the signal sample interval time.
According to the kronecker product, and
δ a ＝[vecv(a(t 1 ))-vecv(a(t 0 )),…,vecv(a(t s ))-vecv(a(t s-1 ))] T ,
Figure BDA00026798501500000910
the above formula can be simplified to obtain:
Figure BDA0002679850150000101
Figure BDA0002679850150000102
Figure BDA0002679850150000103
wherein the content of the first and second substances,
Figure BDA0002679850150000104
is a process matrix and satisfies the column full rank,
Figure BDA0002679850150000105
in the form of a matrix of processes,
Figure BDA0002679850150000106
is a process variable matrix;
step 3, obtaining a data-driven CACC control method according to a data-driven-based controller optimization algorithm;
step 3.1: selecting an initial controller gain K for a follower vehicle 0 And a desired threshold σ > 0;
step 3.2: the initial controller model inputs u (t) -K containing interference information 0 x (t) + e (t) at time intervals of [ t [, ] 0 ,t s ]；
Step 3.3: calculating a process variable
Figure BDA0002679850150000107
Satisfy the requirement of
Figure BDA0002679850150000108
Let j ← 0;
step 3.4: p pair by using the formula in step S3 (j) ，K (j+1) Solving is carried out;
step 3.5: j ← j +1, until | P (j) -P (j-1) |＜σ；
Step 3.6: updating the controller model so that u (t) is equal to-K (j) x(t)；
Step 3.7: returning the updating result of the controller u (t);
when in use
Figure BDA0002679850150000109
When the algorithm converges, i.e. it is
Figure BDA00026798501500001010
And
Figure BDA00026798501500001011
respectively converge to the optimum intermediate value P * And an optimal feedback control gain K * ；
Step 4, constructing a following vehicle differential equation according to the dynamic performance of the vehicle, and proving the stability of the following vehicle;
step 4.1: firstly, constructing a following vehicle dynamic equation:
Figure BDA00026798501500001012
wherein [ delta ] | is not more than rho is interfered when the vehicle runs, and is obtained according to the steps of 3.1-3.7, and exists
Figure BDA00026798501500001013
Epsilon is more than 0 to obtain the estimated optimal controller of the vehicle
Figure BDA00026798501500001014
And 4.2: when T is less than or equal to s is less than or equal to T + T,
Figure BDA0002679850150000111
when there is a minimum value epsilon i Time, matrix
Figure BDA0002679850150000112
Is always a Helvzki matrix and finds the constant β i ,λ i Is greater than 0, and satisfies:
Figure BDA0002679850150000113
wherein i is 1,2, …, n;
step 4.3: for the lead car:
Figure BDA0002679850150000114
β 0 ,λ 0 being constant, it is thus demonstrated that the closed loop system of the vehicle is exponentially stable.
Step 5, constructing a transfer matrix, and proving the optimality of the controller;
defining a minimum loss function J according to the minimum loss function proof ⊙ ＝x T (0)P * x (0), as shown in step 3, the state transition matrix phi (tau, t) satisfies that phi (tau, t) is less than or equal to beta e λ(τ-t) ,
Figure BDA0002679850150000115
Definition of
Figure BDA0002679850150000116
Presence of c 1 ,c 2 >0 is a constant number of times, and,
Figure BDA0002679850150000117
wherein
Figure BDA0002679850150000118
Is semi-positive and continuously differentiable, and has an upper limit of
Figure BDA0002679850150000119
Wherein
Figure BDA00026798501500001110
Φ (τ, τ) ═ I, according to the law of the leibuctz integral, we obtain:
Figure BDA00026798501500001111
setting up
Figure BDA00026798501500001112
According to
Figure BDA00026798501500001113
Distributed minimum loss function
Figure BDA00026798501500001114
Satisfy the requirement of
Figure BDA00026798501500001115
Wherein λ is max (Q) is the maximum eigenvalue of the Q matrix, λ min (P) is the minimum eigenvalue of the P matrix, μ is a constant.
Thus, the controller minimum loss function proves to have optimal performance.
In this embodiment, assume that a leading vehicle and 3 following vehicles travel in a straight line on a lane, and in order to study and analyze the influence of disturbance on performance, two cases are considered: the lead vehicle is not disturbed, the lead vehicle is disturbed, and all vehicles of the fleet are disturbed by the sampling signal in the two conditions. The sampling interval is set to 0.2s therein. The initial position is set to p (0) [ -3,8,20,31] T m, initial velocity v (0) [5,8,9,7 ]] T m/s。
Disturbance xi i (t) can be specifically classified into the following two forms:
case 1: without disturbance
ξ i (t)＝0，i＝0,...n.
Case 2: the lead car is disturbed
ξ i (t)＝10*3sin(3*t)，i＝0.
All vehicles being disturbed
ξ i (t)＝0.3∑sin(random(-1000,1000)*t)，i＝0,...,n.
In the simulation, the initial estimation of the disturbance upper bound and the disturbance lower bound of the lead vehicle are respectively
Figure BDA0002679850150000121
And
Figure BDA0002679850150000122
the initial estimation of the disturbance upper bound and the disturbance lower bound of the following vehicle are respectively
Figure BDA0002679850150000123
And
Figure BDA0002679850150000124
the fleet dynamics parameters were set as follows: time constant of engine (tau) i ＝[0.08,0.12,0.14,0.08]) Time constant h i ＝[0.5,0.49,0.51,0.43]Initial feedback control gain set to K 0 ＝[-0.5,-0.5,0]. In the simulation, the length of the vehicle was ignored.
Based on the parameters, simulation verification is carried out on the motorcade cooperative braking control method based on the data-driven ADP control theory, and the simulation verification is shown in 3-5. Wherein figure 3 shows K under the proposed controller ij ,P ij And (5) an iterative process. As can be seen from FIG. 3, the intermediate value P ij And a feedback control gain K ij The stability is achieved. FIG. 4 shows the variation of the position error, velocity error and self-acceleration of the following vehicle and the preceding vehicle; it can be seen from fig. 4 that the position error of each vehicle in the platoon may slowly converge smoothly to zero after the controller updates. This process takes approximately 5s or so. We can clearly see that the disturbance is not gradually amplified in the following vehicles and the fleet is able to maintain a steady state. Fig. 5 shows the position error, speed error and self acceleration of the following vehicle and the front vehicle when the head vehicle in the fleet has no disturbance. From fig. 5 it can be seen that the vehicle is considered undisturbedThe distance between the front and the rear-end collision avoidance devices is always kept at a reasonable safe distance, so that the rear-end collision is avoided. Further, the pitch error converges to 0 around 5s, and the magnitude of the pitch error decreases as the vehicle index increases in the fleet. The data-driven ADP cooperative brake controller based on the motorcade can not only ensure the stability of each vehicle, but also ensure the stability of the motorcade. And, the ADP controller based on data driving is robust to disturbances.
The foregoing description is only exemplary of the preferred embodiments of the disclosure and is illustrative of the principles of the technology employed. It will be appreciated by those skilled in the art that the scope of the invention in the embodiments of the present disclosure is not limited to the specific combination of the above-mentioned features, but also encompasses other embodiments in which any combination of the above-mentioned features or their equivalents is made without departing from the inventive concept as defined above. For example, the above features and (but not limited to) technical features with similar functions disclosed in the embodiments of the present disclosure are mutually replaced to form the technical solution.

Claims (1)

1. An adaptive dynamic planning method of an anti-interference CACC system is characterized by comprising the following steps:
step 1, constructing a fixed time interval strategy according to the dynamic performance of a vehicle, and establishing a longitudinal dynamic model of the vehicle by adopting a one-way communication structure;
in the step 1, the vehicle longitudinal dynamics model does not contain a lead vehicle, and the inter-vehicle distance error of the ith vehicle is defined as delta p i (t) having:
Δp i (t)＝p i-1 (t)-p i (t)-d s -L,i＝1,2,...,n；
wherein d is s ＝h i v i (t)+r i Is the desired inter-vehicle distance, h i Is a constant headway, v i (t) is the speed of the ith vehicle at time t, r i Fixed inter-vehicle distance, p i (t) is the position of the ith vehicle at time t, L is the vehicle length;
the dynamical model of the ith vehicle is the following nonlinear differential equation:
Figure FDA0003633542670000011
wherein, Δ v i (t) is the speed error of the ith vehicle at time t, a i (t) is the acceleration of the ith vehicle at time t, c i (t) is the feedback linearization control law, h i Constant headway is constant, f i (v i ,a i ) Is a non-linear dynamic model of the vehicle,
Figure FDA0003633542670000012
is a constant;
for a lead car, since it has no front car, its kinematic model is defined as follows:
Figure FDA0003633542670000013
Figure FDA0003633542670000014
where σ is the specific mass of air, τ i Is the mechanical time constant, A i ,c di ,d mi And m i The cross-sectional area, the drag coefficient, the mechanical resistance and the mass of the ith vehicle are respectively;
linearizing the model to obtain a feedback linearization control law as follows:
Figure FDA0003633542670000016
the following linearized models were obtained:
Figure FDA0003633542670000015
wherein u is i (t) is an additional control input signal;
adding disturbance xi to the linearized model due to communication failure or external disturbance in the networking environment i (t); the linearization model after adding the disturbance is:
Figure FDA0003633542670000021
wherein
Figure FDA0003633542670000022
ξ i (t) and
Figure FDA0003633542670000023
are respectively disturbance xi i (t) a lower bound and an upper bound;
step 2, setting the whole fleet to be composed of 1 leading vehicle and n following vehicles, respectively constructing controller models of the leading vehicle and the following vehicles, and providing a controller optimization algorithm based on data driving;
the controller model of the lead vehicle in the step 2 is as follows:
u 0 (t)＝-K 0 x 0 (t)
wherein x 0 (t)＝[p 0 (t) v 0 (t) a 0 (t)] T ，p 0 (t)、v 0 (t) and a 0 (t) is the position, speed and acceleration of the lead vehicle at the moment t, and the feedback control rate K of the lead vehicle 0 ＝[k 01 k 02 k 03 ]Wherein k is 01 ，k 02 ，k 03 Respectively are feedback control laws of the position, the speed and the acceleration of the lead vehicle;
the vehicle-following kinetic model is:
Figure FDA0003633542670000024
wherein the content of the first and second substances,
Figure FDA0003633542670000025
i＝1,2,…,n，x i (t)＝[Δp i (t) Δv i (t) a i (t)] T ；Δp i (t) is the position error of the ith vehicle from the target position at time t, Δ v i (t) is the speed error between the ith vehicle and the preceding vehicle at time t, and the controller u i (t)＝-K i x i (t)，K i ＝[k i1 k i1 k i2 ]Respectively following the feedback control laws of the position, the speed and the acceleration of the vehicle, and obtaining the controller after expansion as follows:
u i (t)＝-k i1 Δp i (t)-k i2 Δv i (t)-k i3 a i (t)
the vehicle-following dynamics model is rewritten as:
Figure FDA0003633542670000026
wherein the content of the first and second substances,
Figure FDA0003633542670000027
j＝0,1,…,n，ω i (t)＝D i x i-1 (t)+I i ξ i (t)，A ij is a coefficient matrix of the state inputs of i cars after iteration j times, B i Is a coefficient matrix of control inputs for i cars, D i Is a coefficient matrix of the status inputs of the i-1 vehicle,
Figure FDA0003633542670000028
is the control gain of i cars after iteration j times;
in step 2, the controller u i (t) the optimization algorithm comprises the steps of:
step S1: selecting a minimum loss function according to a control target:
Figure FDA0003633542670000029
wherein Q is blockdiag (Q) 1 ,Q 2 ,…,Q n )，
Figure FDA00036335426700000210
R＝blockdiag(R 1 ,R 2 ,…,R n ),
Figure FDA00036335426700000211
Figure FDA0003633542670000031
Is the set of states at time t of all vehicles, u ═ u 1 ,u 2 ,…,u n ] T Is the set of control inputs of all vehicles at the time t, the control gain of all vehicles is K * ＝R -1 B T P * Wherein P is * Solved by algebraic Riccati equation;
step S2: obtaining the iteration value of the feedback gain of the step j +1 of the ith vehicle according to the Riccati equation
Figure FDA0003633542670000032
Wherein P is i (j) The intermediate value of step j of the ith vehicle;
step S3: since there is no way to predict the parameter matrix A of the vehicles in the fleet i And B i Then, the solution is solved by the following equation, i.e., [ t, t + δ t [ ]]The difference in time is then the minimum loss function:
Figure FDA0003633542670000033
where δ is the signal sampling interval time;
according to the kronecker product, and
δ a ＝[vecv(a(t 1 ))-vecv(a(t 0 )),…,vecv(a(t s ))-vecv(a(t s-1 ))] T ,
Figure FDA0003633542670000034
the formula is simplified to obtain:
Figure FDA0003633542670000035
Figure FDA0003633542670000036
Figure FDA0003633542670000037
wherein the content of the first and second substances,
Figure FDA0003633542670000038
is a process matrix and satisfies the column full rank,
Figure FDA0003633542670000039
in the form of a matrix of processes,
Figure FDA00036335426700000310
is a process variable matrix;
step 3, obtaining a data-driven CACC control method according to a data-driven-based controller optimization algorithm;
the step 3 specifically comprises the following steps:
step 3.1: selecting an initial controller gain K for a follower vehicle 0 And a desired threshold σ > 0;
step 3.2: the initial controller model inputs u (t) ═ K including interference information 0 x (t) + e (t) at time intervals of [ t [, ] 0 ,t s ]；
Step 3.3: calculating a process variable
Figure FDA0003633542670000041
Until it is satisfied
Figure FDA0003633542670000042
Let j ← 0;
step 3.4: p pair by using the formula in step S3 (j) ，K (j+1) Solving is carried out;
step 3.5: j ← j +1, until | P (j) -P (j-1) |＜σ；
Step 3.6: updating the controller model so that u (t) is equal to-K (j) x(t)；
Step 3.7: returning the updating result of the controller u (t);
when in use
Figure FDA0003633542670000043
When the algorithm converges, i.e. it is
Figure FDA0003633542670000044
And
Figure FDA0003633542670000045
respectively converge to the optimum intermediate value P * And an optimal feedback control gain K * ；
Step 4, constructing a following vehicle differential equation according to the dynamic performance of the vehicle, and proving the stability of the following vehicle;
the step 4 specifically comprises the following steps:
step 4.1: firstly, constructing a following vehicle dynamic equation:
Figure FDA0003633542670000046
wherein [ delta ] | is not more than rho is interfered when the vehicle runs, and is obtained according to the steps of 3.1-3.7, and exists
Figure FDA0003633542670000047
Epsilon is more than 0 to obtain the estimated optimal controller of the vehicle
Figure FDA0003633542670000048
Step 4.2: when T is less than or equal to s is less than or equal to T + T,
Figure FDA0003633542670000049
when there is a minimum value epsilon i Time, matrix
Figure FDA00036335426700000410
Is always a Hulviz matrix and finds the constant β i ,λ i Is greater than 0, and satisfies:
Figure FDA00036335426700000411
wherein i is 1,2, …, n;
step 4.3: for the lead car:
Figure FDA00036335426700000412
β 0 ,λ 0 being constant, it is thus demonstrated that the closed loop system of the vehicle is exponentially stable;
step 5, constructing a transfer matrix to prove the optimality of the controller;
defining a minimum loss function J according to the minimum loss function proof ⊙ ＝x T (0)P * x (0), obtained in step 3, the state transition matrix phi (tau, t) satisfies that phi (tau, t) is less than or equal to beta e λ(τ-t) ,
Figure FDA0003633542670000051
Definition of
Figure FDA0003633542670000052
Presence of c 1 ,c 2 >0 is a constant number of times, and,
Figure FDA0003633542670000053
wherein
Figure FDA0003633542670000054
Is semi-positive and continuously differentiable, and has an upper limit of
Figure FDA0003633542670000055
Wherein
Figure FDA0003633542670000056
Φ (τ, τ) ═ I, according to the law of the leibuctz integral, we obtain:
Figure FDA0003633542670000057
distributed minimum loss function
Figure FDA0003633542670000058
Satisfy the requirement of
Figure FDA0003633542670000059
Wherein λ is max (Q) is the maximum eigenvalue of the Q matrix, λ min (P) is the minimum eigenvalue of the P matrix, μ is a constant;
thus, the controller minimum loss function proves to have optimal performance.
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