CN116243610B - Data-driven vehicle queue fault-tolerant tracking control tracking method and system - Google Patents
Data-driven vehicle queue fault-tolerant tracking control tracking method and system Download PDFInfo
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Abstract
The invention belongs to the technical field of vehicle queue control, and discloses a fault-tolerant tracking control tracking method and system for a data-driven vehicle queue. The invention establishes a biased format dynamic linearization model, namely a PFDL model, aiming at an actual nonlinear vehicle queuing system of sensor faults and DoS attacks, converts a complex nonlinear vehicle queuing system into an equivalent PFDL model by adopting a dynamic linearization technology, approximates the sensor faults by adopting a radial basis function neural network method aiming at the sensor faults in the vehicle queues, finally establishes an elastic fault-tolerant model-free self-adaptive queuing safety controller on the basis, and aims at the problem of non-periodic DoS attacks which are likely to exist in network channels. The invention realizes the goal of synchronous tracking of the positions and the speeds of the leader vehicle and the follower vehicle in the vehicle queuing system.
Description
Technical Field
The invention belongs to the technical field of vehicle queue control, and relates to a fault-tolerant tracking control tracking method and a fault-tolerant tracking control tracking system for a data-driven vehicle queue, which are used for solving the problem of safety control of the vehicle queue affected by sensor faults and aperiodic denial of service attacks.
Background
The vehicle queue control is taken as an intelligent traffic method for coordinating the running process of vehicles, has wide prospect in the aspects of improving the safety of vehicles and improving the traffic capacity of roads, and is widely paid attention to. In the operation process of the fleet, many challenges from the inside and the outside, such as network attack risk problems caused by the communication network, possible faults of the physical and electronic components of the vehicle, and model complexity and uncertainty caused by the complex structure of the vehicle, etc., may be faced. These problems have greatly hindered the way of social progress and sustainable development. As an important development direction of the traffic control field, the intelligent traffic system is born for solving the problems, and the application of the intelligent traffic system is increasingly urgent, so that the intelligent traffic system can reduce traffic jams and improve traffic efficiency.
However, the above-described studies on vehicle control are mostly based on a relatively accurate system model. In fact, due to the complex structure of the actual system, with certain time-varying characteristics and nonlinearity, it is almost impossible to obtain an accurate model in the actual system. With the development of information science and technology, actual processes such as chemical industry, machinery, transportation and the like are also changed over the ground. The production technology and equipment in the industries are large in scale, and the production process is more complex. Modeling using first principles of nature or recognition-based processes becomes more difficult. Thus, conventional model-based control theory has been less applicable to such control problems. The development of data-driven control theory and application based on data for these complex processes has become an urgent issue to be solved.
As one of the data-driven control methods, model-free adaptive control technology has recently received attention from many students and has achieved great research results, providing a theoretical framework for control system design and stability analysis.
In summary, the communication network carries a potential risk of network attacks in vehicle queue control, and it is necessary to take network problems into account. Further, considering that the electronic components (sensors) of the vehicle may malfunction during long-term operation, the malfunction of one or more vehicles may have serious consequences during running. Therefore, achieving fault-tolerant control of the vehicle is a necessary condition for smooth operation of the vehicle queuing system. At the same time the complexity and uncertainty of the vehicle model can also hinder the modeling and control process.
Disclosure of Invention
The invention aims to provide a data-driven vehicle queue fault-tolerant tracking control tracking method so as to realize the self-adaptive queue safety control of an elastic fault-tolerant model-free vehicle queue system under the influence of sensor faults and aperiodic denial of service attacks of the vehicle queue system.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a data-driven vehicle queue fault-tolerant tracking control tracking method comprises the following steps:
step 1, establishing a dynamics equation of a leader vehicle and a follower vehicle in a vehicle queue system;
step 2, obtaining discrete system equations of the leader vehicle and the follower vehicle based on the dynamics equation obtained in the step 1;
step 3, introducing variable PG parameters for auxiliary error analysis into the obtained discrete system equations of the leader vehicle and the follower vehicle, and reconstructing the output of the vehicle queue system by using a biased format dynamic linearization model;
step 4, designing a PG parameter estimator for estimating PG parameters in the partial format dynamic linearization model, and simultaneously introducing an observer and a controller algorithm to control a vehicle queue system;
step 5, approximating the sensor faults by using a radial basis function neural network, re-representing the output with faults by using an approximate fault function, and obtaining a fault-tolerant model-free self-adaptive queue controller;
step 6, on the basis of step 5, considering the aperiodic DoS attack in the network channel, providing an attack index function for indicating whether the attack occurs or not, and providing a corresponding attack compensation mechanism;
and 7, constructing an elastic fault-tolerant model-free self-adaptive queue safety controller by combining the step 5 and the step 6, and realizing synchronous tracking of the positions and the speeds of the leader vehicle and the follower vehicle in the vehicle queue system.
In addition, on the basis of the data-driven vehicle queue fault-tolerant tracking control tracking method, the invention also provides a data-driven vehicle queue fault-tolerant tracking control tracking system which is adaptive to the data-driven vehicle queue fault-tolerant tracking control tracking method, and the data-driven vehicle queue fault-tolerant tracking control tracking system adopts the following technical scheme:
a data-driven vehicle queue fault-tolerant tracking control tracking system, comprising:
the system comprises a dynamics equation construction module, a dynamics equation generation module and a dynamics equation generation module, wherein the dynamics equation construction module is used for establishing dynamics equations of a leader vehicle and a follower vehicle in a vehicle queue system;
the discrete system equation construction module is used for obtaining discrete system equations of the leader vehicle and the follower vehicle;
the system output reconstruction module is used for reconstructing the output of the vehicle queue system by using a partial format dynamic linearization model according to variable PG parameters for introducing auxiliary error analysis in the discrete system equations of the leader vehicle and the follower vehicle;
the system model parameter solving module is used for designing a PG parameter estimator for estimating PG parameters in the partial format dynamic linearization model, and simultaneously introducing an observer and a controller algorithm to control the vehicle queue system;
the fault-tolerant model-free self-adaptive queue control module is used for approximating the sensor faults according to the radial basis function neural network, re-representing the output with the faults by using an approximate fault function, and obtaining a fault-tolerant model-free self-adaptive queue controller;
the attack compensation mechanism construction module is used for providing an attack index function according to the aperiodic DoS attack in the network channel, and is used for indicating whether the attack occurs or not and providing a corresponding attack compensation mechanism;
and the synchronous tracking control module is used for constructing an elastic fault-tolerant model-free self-adaptive queue safety controller and realizing synchronous tracking control of the position and the speed of a leader vehicle by a follower vehicle in the vehicle queue system.
In addition, on the basis of the data-driven vehicle queue fault-tolerant tracking control tracking method, the invention further provides computer equipment which comprises a memory and one or more processors.
The memory stores executable code, and the processor is used for realizing the steps of the data-driven vehicle queue fault-tolerant tracking control tracking method when executing the executable code.
In addition, on the basis of the data-driven vehicle queue fault-tolerant tracking control tracking method, the invention further provides a computer-readable storage medium on which a program is stored. The program, when executed by the processor, is configured to implement the steps of the data-driven vehicle queue fault-tolerant tracking control tracking method described above.
Compared with the prior art, the invention has the following advantages:
as described above, the present invention is directed to a method and system for fault-tolerant tracking control of a data-driven vehicle queue. Aiming at the actual nonlinear vehicle queue system of sensor faults and DoS attacks, a biased format dynamic linearization model, namely a PFDL model, is established according to actual physical significance, a complex nonlinear vehicle queue system is converted into an equivalent PFDL model by adopting a dynamic linearization technology, the sensor faults in a vehicle queue are approximated by adopting a radial basis function neural network method, an elastic fault-tolerant model-free self-adaptive queue safety controller FT-MFAPSC is finally established on the basis, and aiming at the problem of non-periodic DoS attacks possibly existing in network channels, an attack compensation mechanism is provided, so that the problem of vehicle queue tracking control under the non-periodic DoS attacks is solved. The invention realizes the goal of synchronous tracking of the positions and the speeds of the leader vehicle and the follower vehicle in the vehicle queuing system.
Drawings
FIG. 1 is a flow chart of a data driven vehicle queue fault tolerant tracking control tracking method in an embodiment of the invention.
Fig. 2 is a diagram of a vehicle alignment system contemplated by the present invention.
FIG. 3 is a schematic diagram of a partial format dynamic linearization model of a vehicle alignment system contemplated by the present invention.
FIG. 4 is a block diagram of a vehicle queuing system for FT-MFAPSC under an aperiodic DoS attack contemplated by the present invention.
Fig. 5 is a schematic diagram of an aperiodic DoS attack contemplated by the present invention.
Detailed Description
Example 1
In order to solve the problem of safety control of a vehicle queue affected by sensor faults and aperiodic denial of service attacks, the embodiment provides a data-driven vehicle queue fault-tolerant tracking control tracking method.
As shown in fig. 1, the data-driven vehicle queue fault-tolerant tracking control tracking method includes the following steps:
and 1, establishing a dynamics equation of a leader vehicle and a follower vehicle in the vehicle queue system.
(1)
Wherein, the liquid crystal display device comprises a liquid crystal display device,、respectively representing the position and speed of the leader vehicle,as a time-varying nonlinear function; the kinetic equation for the ith follower vehicle is as follows:
(2)
wherein the index i indicates the ith following vehicle,n represents the number of following vehicles;、、is the position, speed and mass of the ith following vehicle;a control input for the i-th following vehicle representing a traction/braking force of the i-th following vehicle;resistance for the ith following vehicle, including throttle, mechanical transmission friction, and aerodynamic resistance;is aboutIs an unknown function of (a).
And 2, obtaining discrete system equations of the leader vehicle and the follower vehicle based on the dynamics equation obtained in the step 1.
The discrete system equations for a follower vehicle are described as:
(3)
wherein, the liquid crystal display device comprises a liquid crystal display device,in order to sample the period of time,、respectively represent the firstVehicle bodyThe position and speed of the moment in time,、、respectively represent the firstVehicle bodyPosition, velocity and acceleration at time.Represent the firstVehicle bodyInput of time.Representation ofIs used to determine the degree of freedom of the function,representation ofIs an unknown function of (a).
The discrete system equations for the leader vehicle are:
(4)
wherein, the liquid crystal display device comprises a liquid crystal display device,、representing leader vehicles respectivelyThe position and speed of the moment;、representing leader vehicles respectivelyPosition of time of dayAnd speed.
And 3, introducing variable PG parameters for auxiliary error analysis into the obtained discrete system equations of the leader vehicle and the follower vehicle, and reconstructing the output of the vehicle queue system by using a partial format dynamic linearization model.
Introducing variables for auxiliary error analysis, and designing an output tuning factor，The selection of (c) will be explained in detail later.
Reconstructing the output of the follower vehicle in the vehicle queuing system as:
；
wherein, the liquid crystal display device comprises a liquid crystal display device,the output at the time of the i-th following vehicle k+1 is indicated.
Reconstructing the output of a leader vehicle in the vehicle queuing system as:
。
wherein, the liquid crystal display device comprises a liquid crystal display device,indicating the output of the leader vehicle at time k. Taking into account the limitations of the actual physical structure of the vehicle, the leader increases the vehicle outputIt is a matter of course that it is not possible to provide a solution,。
assuming a constant existsSo thatThe following redefined vehicle queue system outputs are obtained:
(5)
wherein:
(6)
(7)
(8)
introducing a parameter L as a control inputWhen the linear length coefficient of (a)When the partial format dynamic linearization model is converted into a tight format dynamic linearization model, the following formula is defined:
；
。
wherein, the liquid crystal display device comprises a liquid crystal display device,a vector representing the traction/braking force composition from time k to time k-L+1;representing traction/braking force from time k to time k-L +1And (5) a vector formed by increment.Representing the input increment at time k of the ith vehicle,，representing the input delta at time k-L +1 for the ith vehicle,represent the firstInput at time k-L+1 of the vehicle.
Assuming a nonlinear function、Is about、、The pseudo partial derivative PG is continuous and nonlinear functionMeets the generalized Li Puxi z, namely、If (3)The method comprises the steps of carrying out a first treatment on the surface of the Then:
wherein。
For nonlinear systemsWhen the above assumption is satisfied andfind a time-varying PG parameter vectorSo thatConverting into the following partial format dynamic linearization model:
(9)
wherein the method comprises the steps of，Bounded and of；Is that1 st to L th elements of (b).
As shown in fig. 3, it is known from redefined system outputAnd (3) with、and In relation to, among other things,andrespectively relate toAndis a non-linear function of (2).
Andand (3) withThe value of the i-th following vehicle itself at the moment and the control input are related.
Thus, by selecting an appropriate linearization length factorCan be used forExpressed as in the pastItems relating to control inputs at various moments, i.e. associated withAnd (5) correlation. WhileAndthe relation between the two is reflected by a pseudo partial derivative parameter, so the pseudo partial derivative PG parameter is the key of the PFDL-based vehicle queue system.
Based on the differential median theorem, we next further get:
(10)
wherein:
(11)
order theThe partial format dynamic linearization model is rewritten as:
(12)
wherein, the liquid crystal display device comprises a liquid crystal display device,an input increment representing the i-th vehicle k-1 time;and satisfy the following。
In the above, giveAnda relationship between; based on the above work, the design process of the elastic fault-tolerant model-free self-adaptive queue safety controller can be completed only by the I/O data.
And 4, designing a PG parameter estimator for estimating PG parameters in the partial format dynamic linearization model, and simultaneously introducing an observer and a controller algorithm to control the vehicle queue system.
In analogy to the general PFDL-based control algorithm, the PG parameters of the vehicle are not available, so the present invention designs a PG parameter estimator to estimate the PG parameters, the ith vehicle estimator algorithm is as follows:
(13)
wherein, the liquid crystal display device comprises a liquid crystal display device,、the estimated values of PG parameters at the k moment and the k-1 moment of the ith vehicle are respectively shown;the step size coefficient is represented as such,representing the weight coefficient.
In addition, the observer is added to observe output data, so that the controller algorithm is more universal, and the observer algorithm is as follows:
(14)
wherein, the liquid crystal display device comprises a liquid crystal display device,、output estimates representing times k +1 and k of the vehicle,representing the observer gain. Vehicle queuing system as shown in fig. 2, the vehicle queuing system of the invention establishes an elastic fault-tolerant model-free adaptive queuing security controller FT-MFAPSC for a vehicle queuing system subject to sensor faults and aperiodic DoS attacks.
To optimize tracking control performance, an optimal performance function for the vehicle queuing system is defined as follows:
(15)
wherein, the liquid crystal display device comprises a liquid crystal display device,representing an optimal performance function;as the weight coefficient of the light-emitting diode,is the safe distance between the ith following vehicle and the leader vehicle.
The optimal performance function consists of two parts, namely a second termIn order to enable smooth changes in the control input. First itemThe tracking control performance is optimized on the basis.
According to the extremum optimizing condition, the controller algorithm with the self-adaptive structure is obtained as follows:
(16)
wherein the method comprises the steps ofIs a step size coefficient.
The invention aims at the estimation of the pseudo-gradient parameter vector obtained by using an estimator in a low conservation and no-model self-adaptive control (MFAC) algorithm based on an observer provided by a vehicle queue system, and solves the problem that the pseudo-gradient parameter is unavailable. Compared with the traditional pseudo-gradient algorithm, the method has the advantages that the observer is introduced to eliminate the limitation of unchanged pseudo-gradient parameter sign, and the conservation is reduced.
And 5, approximating the sensor faults by using a radial basis function neural network, re-representing the output with faults by using an approximate fault function, and obtaining the fault-tolerant model-free self-adaptive queue controller.
In practical systems, damage to vehicle components often results in failure of the system during operation.
The invention aims at the sensor fault unfolding research in the vehicle queue system, and researches how to continue to ensure the control effect under the condition of the sensor fault, which is also a typical fault problem.
Radial Basis Function Neural Networks (RBFNN) are one of the better approaches to functions. Approximation of sensor faults for an entire vehicle queuing system using a radial basis function neural network, fault approximation errorsIs defined as:
(17)
wherein, the liquid crystal display device comprises a liquid crystal display device,andthe actual fault function and the approximate fault function of the sensor, respectively.
Then, a neural network approximation error function is definedThe following are provided:
(18)
basis functions in hidden layers of neural networksThe method comprises the following steps:
(19)
wherein, the liquid crystal display device comprises a liquid crystal display device,the number of nodes is indicated and,is an output function of the neural network;the functions in the hidden layers are represented separately, and the specific equations are shown in equation (20).
Specifically, the Gaussian function is selected asNamely, expressed as:
(20)
wherein, the liquid crystal display device comprises a liquid crystal display device,，is the firstThe center of the individual neurons is referred to as the center,is the width of the basis function.
Based on formulas (17) to (20), the approximation function given for the sensor fault is as follows:
(21)
wherein the method comprises the steps ofIs provided with a threshold valueIs used for the output layer weight factor of (a),which respectively represent the positions of 1, …,output layer weighting factors of individual neurons, andthe update rule of (2) is as follows:
。
wherein, the liquid crystal display device comprises a liquid crystal display device,is the learning rate. To facilitate writing, willAbbreviated asSo the rewrite is:
(22)
the convergence of the radial basis function algorithm is demonstrated by means of the Lyapunov function, and the following is obtained:
(23)
wherein, the liquid crystal display device comprises a liquid crystal display device,is a constant.
Based on radial basis function neural network, usingApproximation toSensor failure; the output with failure is expressed as:
(24)
wherein, the liquid crystal display device comprises a liquid crystal display device,representing the output of the ith vehicle with the fault.
Then, the following fault-tolerant model-free adaptive queue controllers are obtained according to the formulas (13) to (16) and (24):
(25)
(26)
(27)
wherein, the liquid crystal display device comprises a liquid crystal display device,indicating that the leader vehicle has a faulty output.
And 6, on the basis of the step 5, considering the aperiodic DoS attack in the network channel, providing an attack index function for indicating whether the attack occurs or not, and providing a corresponding attack compensation mechanism.
Fig. 4 is a system block diagram of the FT-MFAPSC. As can be seen from fig. 4, data packets are transmitted over a networkAn attacker blocks data transmission from the sensor to the controller by attacking the network channel.
The aperiodic DoS attack scheme is shown in fig. 5. Wherein:represent the firstAt the beginning of the time of the secondary attack,is the end time. The gray area indicates that the system is currently being attacked by DoS, while the white area indicates that the system is not currently being attacked by DoS. Will beAndrespectively abbreviated asAnd。
the invention provides the following attack index functionTo indicate whether an attack has occurred, the attack compensation mechanism is as follows:
(28)
wherein, the liquid crystal display device comprises a liquid crystal display device,an attack indicator function indicates whether an attack has occurred.
Represent the firstThe end time of the secondary attack is the time,andrepresent the firstThe starting and ending moments of the secondary attack,represent the firstThe number of attack periods is one,represent the firstSleep periods.
The aggregate of all attack periods, i.e. in the intervalIn (a)All times of (3)Is set of (a)Expressed as:
(29)
wherein N represents a non-negative integer; obviously, when DoS attacks do not occur, the set of all time intervals is as follows:
(30)
wherein, the liquid crystal display device comprises a liquid crystal display device,is an initial attack parameter for handling the situation where the vehicle queuing system is initially attacked,is an attack duration coefficient to be determined; therefore, an attack compensation mechanism is proposed as follows:
(31)
wherein, the liquid crystal display device comprises a liquid crystal display device,representing the output after the compensation of the attack at time k of the ith vehicle with the fault,the output after the compensation is attacked at the moment k-1 of the ith vehicle with the fault.
Representing the estimated value of the pseudo-bias parameter after the i-th vehicle with fault attack compensation at the moment k,and (5) representing the estimated value of the pseudo-bias parameter after the i-th vehicle k-1 moment attack compensation with the fault.
And 7, constructing an elastic fault-tolerant model-free self-adaptive queue safety controller by combining the step 5 and the step 6, and realizing synchronous tracking of the position and the speed of the leader vehicle by the follower vehicle in the vehicle queue system.
The design of the elastic fault-tolerant model-free self-adaptive queue safety control controller is as follows:
(32)
(33)
(34)
wherein, the liquid crystal display device comprises a liquid crystal display device,is a normal number, has smaller value,representing the estimated initial value of the pseudo-bias guide of the ith vehicle.
As shown in fig. 4, the method of the present invention contemplates a vehicle consist of n+1 vehicles, wherein the front of the vehicle consist has a leader vehicle behind itA vehicle follower vehicle. First of all speed and displacement data measured by sensors of a vehicle queuing systemBecause PG parameters in the partial format dynamic linearization are not available, a PG parameter estimator is designed at the sensor end, and therefore, the data packetAnd transmitting to the controller through a network. Considering that there is a non-periodic DoS attack in the network channel, an attacker blocks data transmission from the sensor to the controller by attacking the network channel, therefore the invention proposes an attack compensation mechanism to make the data packet after compensation when transmitted to the controllerAt the same time consider pairs ofThe controller based on the observation period for observation makes the designed observer have more universality, and the controller obtains the output through calculationThe system acts on an actuator to control the vehicle queue system so as to achieve the aim of synchronously tracking the positions and the speeds of the follower vehicle and the leader vehicle.
Example 2
Embodiment 2 describes a data-driven vehicle train fault-tolerant tracking control tracking system based on the same inventive concept as the data-driven vehicle train fault-tolerant tracking control tracking method in embodiment 1 described above.
A data-driven vehicle queue fault-tolerant tracking control tracking system, comprising:
the system comprises a dynamics equation construction module, a dynamics equation generation module and a dynamics equation generation module, wherein the dynamics equation construction module is used for establishing dynamics equations of a leader vehicle and a follower vehicle in a vehicle queue system;
the discrete system equation construction module is used for obtaining discrete system equations of the leader vehicle and the follower vehicle;
the system output reconstruction module is used for reconstructing the output of the vehicle queue system by using a partial format dynamic linearization model according to variable PG parameters for introducing auxiliary error analysis in the discrete system equations of the leader vehicle and the follower vehicle;
the system model parameter solving module is used for designing a PG parameter estimator for estimating PG parameters in the partial format dynamic linearization model, and simultaneously introducing an observer and a controller algorithm to control the vehicle queue system;
the fault-tolerant model-free self-adaptive queue control module is used for approximating the sensor faults according to the radial basis function neural network, re-representing the output with the faults by using an approximate fault function, and obtaining a fault-tolerant model-free self-adaptive queue controller;
the attack compensation mechanism construction module is used for providing an attack index function according to the aperiodic DoS attack in the network channel, and is used for indicating whether the attack occurs or not and providing a corresponding attack compensation mechanism;
and the synchronous tracking control module is used for constructing an elastic fault-tolerant model-free self-adaptive queue safety controller and realizing synchronous tracking control of the position and the speed of a leader vehicle by a follower vehicle in the vehicle queue system.
It should be noted that, in the fault-tolerant tracking control tracking system for a data-driven vehicle queue, the implementation process of the functions and roles of each functional module is specifically described in the implementation process of the corresponding steps in the method in the above embodiment 1, and will not be described herein.
Example 3
Embodiment 3 describes a computer apparatus for implementing the steps of the data-driven vehicle queue fault-tolerant tracking control tracking method described in embodiment 1 above.
The computer device includes a memory and one or more processors. Executable code is stored in the memory for implementing the steps of the data driven vehicle queue fault tolerant tracking control tracking method when the executable code is executed by the processor.
In this embodiment, the computer device is any device or apparatus having data processing capability, which is not described herein.
Example 4
Embodiment 4 describes a computer-readable storage medium for implementing the steps of the data-driven vehicle queue fault-tolerant tracking control tracking method described in embodiment 1 above.
The computer-readable storage medium of this embodiment 4 has stored thereon a program for implementing the steps of the data-driven vehicle queue fault-tolerant tracking control tracking method when executed by a processor.
The computer readable storage medium may be an internal storage unit of any device or apparatus having data processing capability, such as a hard disk or a memory, or may be an external storage device of any device having data processing capability, such as a plug-in hard disk, a Smart Media Card (SMC), an SD Card, a Flash memory Card (Flash Card), or the like, which are provided on the device.
The foregoing description is, of course, merely illustrative of preferred embodiments of the present invention, and it should be understood that the present invention is not limited to the above-described embodiments, but is intended to cover all modifications, equivalents and alternatives falling within the spirit and scope of the present invention as defined by the appended claims.
Claims (2)
1. A data-driven vehicle queue fault-tolerant tracking control tracking method is characterized by comprising the following steps:
step 1, establishing a dynamics equation of a leader vehicle and a follower vehicle in a vehicle queue system;
step 2, obtaining discrete system equations of the leader vehicle and the follower vehicle based on the dynamics equation obtained in the step 1;
step 3, introducing variable PG parameters for auxiliary error analysis into the obtained discrete system equations of the leader vehicle and the follower vehicle, and reconstructing the output of the vehicle queue system by using a biased format dynamic linearization model;
step 4, designing a PG parameter estimator for estimating PG parameters in the partial format dynamic linearization model, and simultaneously introducing an observer and a controller algorithm to control a vehicle queue system;
step 5, approximating the sensor faults by using a radial basis function neural network, and re-representing the output with faults by using an approximate fault function to obtain a fault-tolerant model-free self-adaptive queue controller;
step 6, on the basis of step 5, considering the aperiodic DoS attack in the network channel, providing an attack index function for indicating whether the attack occurs or not, and providing a corresponding attack compensation mechanism;
step 7, combining the step 5 and the step 6, constructing an elastic fault-tolerant model-free self-adaptive queue safety controller, so as to realize synchronous tracking of the positions and speeds of a leader vehicle and a follower vehicle in a vehicle queue system;
in the step 1, the dynamics of the vehicle are described as follows:
the kinetic equation of the leader vehicle is:
wherein x is 0 (t)、Representing the leader vehicles respectivelyPosition, speed, f 0 (t) is a time-varying nonlinear function; the kinetic equation for the ith follower vehicle is as follows:
wherein the subscript i represents the i-th following vehicle, i=1,..n, n represents the number of following vehicles;
x i (t)、v i (t)、is the position, speed and mass of the ith following vehicle;
a control input for the i-th following vehicle representing a traction/braking force of the i-th following vehicle;
resistance for the ith following vehicle, including throttle, mechanical transmission friction, and aerodynamic resistance;
is about x i An unknown function of (t);
in the step 2, the discrete system equation of the follower vehicle is described as:
wherein T is 0 For sampling period, x i (k+1)、v i (k+1) represents the position and speed, x, of the ith vehicle at time k+1, respectively i (k)、v i (k)、a i (k) Respectively are provided withRepresenting the position, speed and acceleration of the ith vehicle at time k;
u i (k) An input representing a time k of an ith vehicle;
f i,v (v i (k) With respect to v) i (k) Unknown function f i,x (x i (k) With respect to x) i (k) Is an unknown function of (2);
the discrete system equations for the leader vehicle are:
wherein x is 0 (k+1)、v 0 (k+1) represents the position and speed of the leader vehicle at time k+1, respectively;
x 0 (k)、v 0 (k) Respectively representing the position and the speed of the leader vehicle at the moment k;
in the step 3, a variable for assisting error analysis is introduced, and an output tuning factor theta is designed i (k)；
Reconstructing the output of the follower vehicle in the vehicle queuing system as:
y i (k+1)＝x i (k+1)+θ i (k)v i (k+1)；
wherein y is i (k+1) represents an output at time k+1 of the i-th following vehicle;
reconstructing the output of a leader vehicle in the vehicle queuing system as:
y 0 (k)＝x 0 (k)+θ i (k)v 0 (k)；
wherein y is 0 (k) Representing the output of the leader vehicle at time k; taking into account the limitations of the actual physical structure of the vehicle, the leader vehicle outputs an increment deltay 0 (k) Is bounded, deltay 0 (k)＝y 0 (k)-y 0 (k-1)；
Assuming that a constant g exists i > 0, such that |Δy 0 (k)|≤g i The following redefined vehicle queue system outputs are obtained:
wherein:
introducing a parameter L as a control input u i (k) And defines the following formula:
ΔU i (k)＝[Δu i (k),…,Δu i (k-L+1)] T ；
wherein U is i (k) A vector representing the traction/braking force composition from time k to time k-L+1; deltaU i (k) A vector representing the delta composition of traction/braking force from time k to time k-L+1;
Δu i (k) Input delta, deltau, representing the i-th vehicle at time k i (k)＝u i (k)-u i (k-1)，Δu i (k-L+1) represents the input increment at time k-L+1 of the ith vehicle, u i (k-L+1) represents an input at time k-L+1 of the i-th vehicle;
assuming a nonlinear function F i,x (·)、F i,v (. Cndot.) is related to Deltau i (k)、...、Δu i The (k-L) pseudo-partial derivative PG is continuous and is a nonlinear function y i (k) Meets the generalized Li Puxi z, namelyk n 0 or more, if k m ≠k n ，U i (k m )≠U i (k n )；
Then |y i (k m +1)-y i (k n +1)|≤β i ‖U i (k m )-U i (k n ) II, wherein beta i ＞0；
For nonlinear systems y i (k) When the above assumption is satisfied andfind a time-varying PG parameter vector>So that y i (k) Converting into the following partial format dynamic linearization model:
wherein Δy i (k+1)＝y i (k+1)-y i (k),Φ i (k)＝[φ i,1 (k),…,φ i,L (k)] T ，Φ i (k) Bounded and II phi i (k)‖≤β i ；φ i,1 (k),…,φ i,L (k) Is phi i (k) 1 st to L th elements of (b);
based on the differential median theorem, we next further get:
wherein:
order theThe partial format dynamic linearization model is rewritten as:
wherein Deltau i (k-1) represents an input increment at time k-1 of the i-th vehicle;
Ψ i (k)＝[ψ i,1 (k),…,ψ i,L (k)] T and meet +. i (k)‖≤β i ；
In the step 4, a PG parameter estimator is designed to estimate PG parameters, and the ith vehicle estimator algorithm is as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,the estimated values of PG parameters at the k moment and the k-1 moment of the ith vehicle are respectively shown;
τ i representing step size coefficients, lambda i Representing the weight coefficient; adding an observer to observe output data, wherein an observer algorithm is as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,output estimated value representing vehicle k+1 time and k time, W i Representing observer gain; to optimize tracking control performance, an optimal performance function for the vehicle queuing system is defined as follows:
wherein y [ u ] i (k)]Representing an optimal performance function;
ω i as the weight coefficient, d i,0 > 0 is the safe distance between the ith following vehicle and the leader vehicle;
according to the extremum optimizing condition, the controller algorithm with the self-adaptive structure is obtained as follows:
wherein ρ is i,j Is a step size coefficient;
in the step 5, a radial basis function neural network is utilized to approximate the sensor faults of the vehicle queue system;
error of fault approximationIs defined as:
wherein, the liquid crystal display device comprises a liquid crystal display device,and->The actual fault function and the approximate fault function of the sensor are respectively;
then, the neural network approximation error function σi (k) is defined as follows:
basis functions in hidden layers of neural networksThe method comprises the following steps:
wherein, the liquid crystal display device comprises a liquid crystal display device,indicating the number of nodes, h i (k) Is an output function of the neural network; />Respectively representing functions in the hidden layers, wherein the equation is shown as a formula (20); selecting the Gaussian function to be +.>Expressed as:
wherein, the liquid crystal display device comprises a liquid crystal display device,η i,j is the center of the jth neuron, ζ i,j Is the width of the basis function;
based on formulas (17) to (20), the approximation function given for the sensor fault is as follows:
wherein the method comprises the steps ofIs with threshold +.>Is used for the output layer weight factor of (a),respectively represent +.>Output layer weighting factors of individual neurons, and w i (k) The update rule of (2) is as follows:
the convergence of the radial basis function algorithm is demonstrated by means of the Lyapunov function, and the following is obtained:
wherein θ i Is a constant;
based on radial basis function neural network, usingApproximation sensor failure; the output with failure is expressed as:
wherein, the liquid crystal display device comprises a liquid crystal display device,representing an output of the ith vehicle with the fault;
then, the following fault-tolerant model-free adaptive queue controllers are obtained according to the formulas (13) to (16) and (24):
wherein, the liquid crystal display device comprises a liquid crystal display device,an output indicating that the leader vehicle is faulty;
in the step 6, the attack compensation mechanism is as follows:
wherein l i (k) An attack index function is used for indicating whether an attack occurs;
represents the end time of the m-1 th attack, < >>And->Indicating the start and end time of the mth attack, < >>Represents the mth attack period,/->Representing an mth sleep period;
the set of all attack periods, i.e. in interval 0, k]Middle l m (k) Set Γ for all time instants k of =0 0 (0, k) is expressed as:
wherein N represents a non-negative integer; obviously, when DoS attacks do not occur, the set of all time intervals is as follows:
wherein Γ is 0 The initial attack parameter is more than 0, and is used for processing the situation that the vehicle queue system is attacked at the beginning, and the attack duration coefficient to be determined is gamma more than 1; therefore, an attack compensation mechanism is proposed as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,representing the output after compensation of the i-th vehicle with fault attack at time k,/>Representing the output after attack compensation at the time of the ith vehicle k-1 with the fault;
representing the estimated value of the pseudo-bias parameter after the compensation of the attack at the moment k of the ith vehicle with fault,/and the like>Representing the false partial derivative parameter estimated value after the i-th vehicle k-1 moment attack compensation with faults;
in the step 7, the design of the elastic fault-tolerant model-free self-adaptive queue safety controller is as follows:
wherein mu i Is a normal number of times,representing the estimated initial value of the pseudo-bias guide of the ith vehicle.
2. A data-driven vehicle queue fault-tolerant tracking control tracking system for implementing the data-driven vehicle queue fault-tolerant tracking control tracking method of claim 1,
the data-driven vehicle queue fault-tolerant tracking control tracking system comprises:
the system comprises a dynamics equation construction module, a dynamics equation generation module and a dynamics equation generation module, wherein the dynamics equation construction module is used for establishing dynamics equations of a leader vehicle and a follower vehicle in a vehicle queue system;
the discrete system equation construction module is used for obtaining discrete system equations of the leader vehicle and the follower vehicle;
the system output reconstruction module is used for reconstructing the output of the vehicle queue system by using a partial format dynamic linearization model according to variable PG parameters for introducing auxiliary error analysis in the discrete system equations of the leader vehicle and the follower vehicle;
the system model parameter solving module is used for designing a PG parameter estimator for estimating PG parameters in the partial format dynamic linearization model, and simultaneously introducing an observer and a controller algorithm to control the vehicle queue system;
the fault-tolerant model-free self-adaptive queue control module is used for approximating the sensor faults according to the radial basis function neural network, re-representing the output with the faults by using an approximate fault function, and obtaining a fault-tolerant model-free self-adaptive queue controller;
the attack compensation mechanism construction module is used for providing an attack index function according to the aperiodic DoS attack in the network channel, and is used for indicating whether the attack occurs or not and providing a corresponding attack compensation mechanism;
and the synchronous tracking control module is used for constructing an elastic fault-tolerant model-free self-adaptive queue safety controller and realizing synchronous tracking control of the position and the speed of a leader vehicle by a follower vehicle in the vehicle queue system.
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