CN112034859A - Self-adaptive dynamic planning method of anti-interference CACC system - Google Patents
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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
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:
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 pi(t) having:
Δpi(t)=pi-1(t)-pi(t)-ds-L,i=1,2,...,n
wherein d iss=hivi(t)+riIs the desired inter-vehicle distance, hiIs a constant headway, vi(t) is the speed of the ith vehicle at time t, riFixed inter-vehicle distance, pi(t) is the position of the ith vehicle at time t, and L is the vehicle length;
the dynamical model of the ith vehicle is the following nonlinear differential equation:
wherein, Δ vi(t) is the speed error of the ith vehicle at time t, ai(t) is the acceleration of the ith vehicle at time t, ci(t) is the feedback linearization control law, hiConstant headway is constant, fi(vi,ai) Is a non-linear dynamic model of the vehicle,is a constant;
for a lead car, since it has no front car, its kinematic model is defined as follows:
where σ is the specific mass of air, τiIs the mechanical time constant, Ai,cdi,dmiAnd miThe 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:
the following linearized models were obtained:
wherein u isi(t) is an additional control input signal;
adding disturbance xi to the linearized model due to communication failure or external disturbance in the networking environmenti(t); the linearization model after adding the disturbance is:
the controller model of the lead vehicle is as follows:
u0(t)=-K0x0(t)
wherein x0(t)=[p0(t) v0(t) a0(t)]T,p0(t)、v0(t) and a0(t) is the position, speed and acceleration of the lead vehicle at the moment t, and the feedback control rate K of the lead vehicle0=[k01 k02 k03]Wherein k is01,k02,k03Respectively, the position, the speed and the acceleration of the lead vehicle.
The vehicle-following kinetic model is:
wherein,i=1,2,…,n,xi(t)=[Δpi(t) Δvi(t) ai(t)]T;Δpi(t) is the position error of the ith vehicle from the target position at time t, Δ vi(t) is the speed error between the ith vehicle and the preceding vehicle at time t, and the controller ui(t)=-Kixi(t),Ki=[ki1 ki1 ki2]The feedback control laws respectively follow the position, speed and acceleration of the vehicle. The controller after the unfolding is obtained as follows:
ui(t)=-ki1Δpi(t)-ki2Δvi(t)-ki3ai(t)
the vehicle-following dynamics model is rewritten as:
wherein,j=0,1,…,n,ωi(t)=Dixi-1(t)+Iiξi(t),Aijis a coefficient matrix of the state inputs of i cars after iteration j times, BiIs a coefficient matrix of control inputs for i cars, DiIs a coefficient matrix of the status inputs of the i-1 vehicle,is the control gain for i cars after j iterations.
The controller ui(t) the optimization algorithm comprises the steps of:
step S1: selecting a minimum loss function according to a control target:
wherein Q is blockdiag (Q)1,Q2,…,Qn),R=blockdiag(R1,R2,…,Rn), Is the set of states at time t of all vehicles, u ═ u1,u2,…,un]TIs the set of control inputs of all vehicles at the time t, the control gain of all vehicles is K*=R-1BTP*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 equationWhereinThe 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 fleetiAnd BiThen, the solution is solved by the following equation, i.e., [ t, t + t [ ]]The difference in time is then the minimum loss function:
where is the signal sample interval time.
According to the kronecker product, and
a=[vecv(a(t1))-vecv(a(t0)),…,vecv(a(ts))-vecv(a(ts-1))]T,
the formula is simplified to obtain:
wherein,is a process matrix and satisfies the column full rank,in the form of a matrix of processes,is a process variable matrix;
step 3.1: selecting an initial controller gain K for a follower vehicle0And a desired threshold σ > 0;
step 3.2: the initial controller model inputs u (t) ═ K including interference information0x (t) + e (t) at time intervals of [ t [, ]0,ts];
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 useWhen the algorithm converges, i.e. it isAndrespectively converge to the optimum intermediate value P*And an optimal feedback control gain K*;
step 4.1: firstly, constructing a following vehicle dynamic equation:
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 existsGet the estimated optimal controller of the vehicle > 0
when there is a minimum valueiTime, matrixIs always a Hulviz matrix and finds the constant βi,λiIs greater than 0, and satisfies:
wherein i is 1,2, …, n;
step 4.3: for the lead car:β0,λ0is constant, thus proving that the closed loop system of the vehicle is exponentially stable.
defining a minimum loss function J according to the minimum loss function proof⊙=xT(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 eλ(τ-t),Definition ofPresence of c1,c2>0 is a constant number of times, and,whereinIs semi-positive and continuously differentiable, and has an upper limit ofWhereinΦ (τ, τ) ═ I, according to the law of the leibuctz integral, we obtain:
Wherein λ ismax(Q) is the maximum eigenvalue of the Q matrix, λmin(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) -PijMatrix 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 in the straight lane runs are shown in the graph (a), the following vehicle v2 and the preceding vehicle error condition when the vehicle in the straight lane runs are shown in the graph (b), and the following vehicle v3 and the preceding vehicle error condition when the vehicle in the straight lane runs are shown in the graph (c);
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) -the following vehicle v1 and the preceding 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:
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 pi(t) having:
Δpi(t)=pi-1(t)-pi(t)-ds-L,i=1,2,...,n
wherein d iss=hivi(t)+riIs the desired inter-vehicle distance, hiIs a constant headway, vi(t) is the speed of the ith vehicle at time t, riFixed inter-vehicle distance, pi(t) is the position of the ith vehicle at time t, and L is the vehicle length;
the dynamical model of the ith vehicle is the following nonlinear differential equation:
wherein, Δ vi(t) is the speed error of the ith vehicle at time t, ai(t) is the acceleration of the ith vehicle at time t, ci(t) is the feedback linearization control law, hiConstant headway is constant, fi(vi,ai) Is a non-linear dynamic model of the vehicle,is a constant;
for a lead car, since it has no front car, its kinematic model is defined as follows:
where σ is the specific mass of air, τiIs the mechanical time constant, Ai,cdi,dmiAnd miThe 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:
the following linearized models were obtained:
wherein u isi(t) is an additional control input signal to enable the closed loop system to satisfy the stable reactancePerformance indicators of interference; with this controller, the following two objectives are achieved: 1) linearization of ith vehicle dynamics; 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 environmenti(t); the linearization model after adding the disturbance is:
the controller model of the lead vehicle is as follows:
u0(t)=-K0x0(t)
wherein x0(t)=[p0(t) v0(t) a0(t)]T,p0(t)、v0(t) and a0(t) is the position, speed and acceleration of the lead vehicle at the moment t, and the feedback control rate K of the lead vehicle0=[k01 k02 k03]Wherein k is01,k02,k03Respectively, the position, the speed and the acceleration of the lead vehicle.
The vehicle-following kinetic model is:
wherein,i=1,2,…,n,xi(t)=[Δpi(t) Δvi(t) ai(t)]T;Δpi(t) is the position error of the ith vehicle from the target position at time t, Δ vi(t) is the speed error between the ith vehicle and the preceding vehicle at time t, and the controller ui(t)=-Kixi(t),Ki=[ki1 ki1 ki2]The feedback control laws respectively follow the position, speed and acceleration of the vehicle. The controller after the unfolding is obtained as follows:
ui(t)=-ki1Δpi(t)-ki2Δvi(t)-ki3ai(t)
the vehicle-following dynamics model is rewritten as:
wherein,j=0,1,…,n,Aijis a coefficient matrix of the state inputs of i cars after iteration j times, BiIs a coefficient matrix of control inputs for i cars, DiIs a coefficient matrix of the status inputs of the i-1 vehicle,is the control gain for i cars after j iterations.
The controller ui(t) the optimization algorithm comprises the steps of:
step S1: selecting a minimum loss function according to a control target:
wherein Q is blockdiag (Q)1,Q2,…,Qn),R=blockdiag(R1,R2,…,Rn), Is the set of states at time t of all vehicles, u ═ u1,u2,…,un]TIs the set of control inputs of all vehicles at the time t, the control gain of all vehicles is K*=R-1BTP*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 equationWhereinThe 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 fleetiAnd BiThen, the solution is solved by the following equation, i.e., [ t, t + t [ ]]The difference in time is then the minimum loss function:
where is the signal sample interval time.
According to the kronecker product, and
a=[vecv(a(t1))-vecv(a(t0)),…,vecv(a(ts))-vecv(a(ts-1))]T,
the above formula can be simplified to obtain:
wherein,is a process matrix and satisfies the column full rank,in the form of a matrix of processes,is a process variable matrix;
step 3.1: selecting an initial controller gain K for a follower vehicle0And a desired threshold σ > 0;
step 3.2: the initial controller model inputs u (t) ═ K including interference information0x (t) + e (t) at time intervals of [ t [, ]0,ts];
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 useWhen the algorithm converges, i.e. it isAndrespectively converge to the optimum intermediate value P*And an optimal feedback control gain K*;
step 4.1: firstly, constructing a following vehicle dynamic equation:
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 existsGet the estimated optimal controller of the vehicle > 0
when there is a minimum valueiTime, matrixIs always a Hulviz matrix and finds the constant βi,λiIs greater than 0, and satisfies:
wherein i is 1,2, …, n;
step 4.3: for the lead car:β0,λ0being constant, it is thus demonstrated that the closed loop system of the vehicle is exponentially stable.
defining a minimum loss function J according to the minimum loss function proof⊙=xT(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 eλ(τ-t),Definition ofPresence of c1,c2>0 is a constant number of times, and,whereinIs semi-positive and continuously differentiable, and has an upper limit ofWhereinΦ (τ, τ) ═ I, according to the law of the leibuctz integral, we obtain:
Wherein λ ismax(Q) is the maximum eigenvalue of the Q matrix, λmin(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 undisturbed, 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]Tm, initial velocity v (0) [5,8,9,7 ]]Tm/s。
Disturbance xii(t) can be specifically classified into the following two forms:
case 1: without disturbance
ξi(t)=0,i=0,...n.
Case 2: the lead car is disturbed
ξi(t)=10*3sin(3*t),i=0.
All vehicles being disturbed
ξi(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 respectivelyAndthe initial estimation of the disturbance upper bound and the disturbance lower bound of the following vehicle are respectivelyAndthe fleet dynamics parameters were set as follows: time constant of engine (tau)i=[0.08,0.12,0.14,0.08]) Time constant hi=[0.5,0.49,0.51,0.43]Initial feedback control gain set to K0=[-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 controllerij,PijAnd (5) an iterative process. As can be seen from FIG. 3, the intermediate value PijAnd a feedback control gain KijThe 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 thatUnder the condition of no disturbance, the distance between vehicles always keeps a reasonable safe distance, thereby avoiding the occurrence of rear-end accidents. 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 (6)
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;
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;
step 3, obtaining a data-driven CACC control method according to a data-driven-based controller optimization algorithm;
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 5, constructing a transfer matrix to prove the optimality of the controller;
according to a minimum loss functionProve, define the minimum loss function J⊙=xT(0)P*x (0), obtained in step 3, the state transition matrix Φ (τ, t) satisfiesDefinition ofPresence of c1,c2>0 is a constant number of times, and,whereinIs semi-positive and continuously differentiable, and has an upper limit ofWhereinΦ (τ, τ) ═ I, according to the law of the leibuctz integral, we obtain:
Wherein λ ismax(Q) is the maximum eigenvalue of the Q matrix, λmin(P) is the minimum eigenvalue of the P matrix, μ is a constant;
thus, the controller minimum loss function proves to have optimal performance.
2. The adaptive dynamic programming method for an antijam CACC system as claimed in claim 1, wherein the longitudinal dynamics model of the vehicle in step 1 does not include a lead vehicle, and the inter-vehicle distance error of the i-th vehicle is defined as Δ pi(t) having:
Δpi(t)=pi-1(t)-pi(t)-ds-L,i=1,2,...,n;
wherein d iss=hivi(t)+riIs the desired inter-vehicle distance, hiIs a constant headway, vi(t) is the speed of the ith vehicle at time t, riFixed inter-vehicle distance, pi(t) is the position of the ith vehicle at time t, and L is the vehicle length;
the dynamical model of the ith vehicle is the following nonlinear differential equation:
wherein, Δ vi(t) is the speed error of the ith vehicle at time t, ai(t) is the acceleration of the ith vehicle at time t, ci(t) is the feedback linearization control law, hiConstant headway is constant, fi(vi,ai) Is a non-linear dynamic model of the vehicle,is a constant;
for a lead car, since it has no front car, its kinematic model is defined as follows:
where σ is the specific mass of air, τiIs the mechanical time constant, Ai,cdi,dmiAnd miThe 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:
the following linearized models were obtained:
wherein u isi(t) is an additional control input signal;
adding disturbance xi to the linearized model due to communication failure or external disturbance in the networking environmenti(t); the linearization model after adding the disturbance is:
3. The adaptive dynamic programming method of an antijam CACC system as set forth in claim 1, wherein the controller model of the lead vehicle in step 2 is as follows:
u0(t)=-K0x0(t)
wherein x0(t)=[p0(t) v0(t) a0(t)]T,p0(t)、v0(t) and a0(t) is the position, speed and acceleration of the lead vehicle at the moment t, and the feedback control rate K of the lead vehicle0=[k01 k02 k03]Wherein k is01,k02,k03Respectively are feedback control laws of the position, the speed and the acceleration of the lead vehicle;
the vehicle-following kinetic model is:
wherein,xi(t)=[Δpi(t) Δvi(t) ai(t)]T;Δpi(t) is the position error of the ith vehicle from the target position at time t, Δ vi(t) is the speed error between the ith vehicle and the preceding vehicle at time t, and the controller ui(t)=-Kixi(t),Ki=[ki1 ki1 ki2]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:
ui(t)=-ki1Δpi(t)-ki2Δvi(t)-ki3ai(t)
the vehicle-following dynamics model is rewritten as:
4. The adaptive dynamic programming method of an antijam CACC system as set forth in claim 1, wherein said controller u in step 2i(t) the optimization algorithm comprises the steps of:
step S1: selecting a minimum loss function according to a control target:
wherein Is the set of states at time t of all vehicles, u ═ u1,u2,…,un]TIs the set of control inputs of all vehicles at the time t, the control gain of all vehicles is K*=R-1BTP*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 equationWherein P isi (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 fleetiAnd BiThen, the following equation is used to solve, i.e., [ t ],t+t]The difference in time is then the minimum loss function:
where is the signal sample interval time;
according to the kronecker product, and
a=[vecv(a(t1))-vecv(a(t0)),…,vecv(a(ts))-vecv(a(ts-1))]T,
the formula is simplified to obtain:
5. The adaptive dynamic planning method for an anti-interference CACC system according to claim 1, wherein step 3 specifically comprises the following steps:
step 3.1: selecting an initial controller gain K for a follower vehicle0And a desired threshold σ > 0;
step 3.2: the initial controller model inputs u (t) ═ K including interference information0x (t) + e (t) at time intervals of [ t [, ]0,ts];
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);
6. The adaptive dynamic planning method for an anti-jamming CACC system according to claim 1, wherein step 4 specifically includes the steps of:
step 4.1: firstly, constructing a following vehicle dynamic equation:
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 existsGet the estimated optimal controller of the vehicle > 0
when there is a minimum valueiTime, matrixIs always a Hulviz matrix and finds the constant βi,λiIs greater than 0, and satisfies:
wherein i is 1,2, …, n;
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