Distributed model prediction anti-interference control method for vehicle queue

Abstract

The invention discloses a distributed model prediction anti-interference control method for a vehicle queue. The method comprises the following steps: obtaining a distributed model prediction controller objective function; obtaining a nominal expected acceleration control law of the distributed model prediction controller based on a KKT condition method; obtaining an uncertain disturbance value caused by unmodeled characteristics of the vehicle queue control system; calculating an expected acceleration; and carrying out distributed model prediction anti-interference control. Based on a following vehicle longitudinal dynamic model containing an uncertain disturbance term, a time lag dynamic model considering communication network time lag under an asynchronous sampling mechanism is established, and a designed compensation controller can estimate uncertain disturbance of a following vehicle caused by unmodeled characteristics of a system in real time. And the anti-interference capability of the vehicle queue controller is improved, so that the control precision, stability and robustness are improved.

Description

Technical Field

[0001] The present invention relates to a vehicle platoon longitudinal tracking control technology considering asynchronous sampling and communication network time delay, and in particular to a distributed model predictive controller (DMPC) considering disturbance compensation of a distributed extended state observer (DESO). Background Art

[0002] Platooning vehicles can reduce the distance between vehicles without compromising driving safety, thereby improving commuting efficiency. Furthermore, smaller distances between vehicles reduce air resistance experienced by vehicles in the platoon, making vehicles more energy-efficient. Vehicle platooning control systems, which can be implemented using vehicle-to-vehicle (V2V) communication, are a classic type of networked control system that relies heavily on network communication and inevitably introduces communication lag. Furthermore, sensor / sampler jitter and aging can make periodic sampling strategies incompatible with actual communication transmission conditions, often manifesting as non-fixed sampling times. This results in uncertainty in the sampled data packets transmitted over the network, which impacts the control performance of the vehicle platoon. Furthermore, uncertain disturbances caused by unmodeled components of the vehicle platooning control system can also degrade controller performance and stability margins. These uncertain disturbances can affect the control performance of the platoon controller, further degrading platoon tracking and potentially leading to traffic accidents. Therefore, it is necessary to model these uncertain disturbances to simulate real-world disturbances.

[0003] Traditional queue controllers include model predictive controller, robust H ∞ Controllers, such as those for proportional-integral-derivative controllers, are designed based on periodic sampling strategies. This can be achieved under ideal communication conditions, but this is clearly inconsistent with actual communication conditions. Therefore, it is necessary to consider sampling time uncertainty when designing controllers. Furthermore, when solving distributed model predictive controllers, the time it takes for a quadratic programming (QP) solver can reduce the controller's real-time performance, necessitating the design of a more real-time solution method.

[0004] The extended state observer (ESO) is a simple and robust disturbance observer that estimates the value of unmodeled disturbances in vehicle platoon control systems and feeds them back to the controller for compensation. A distributed ESO can estimate the disturbances caused by communication network delays and unmodeled characteristics of the platoon dynamics model for each following vehicle in an asynchronous sampling environment. Therefore, it is necessary to develop a distributed model predictive anti-disturbance control method for vehicle platoons that considers disturbance compensation using the distributed ESO. Summary of the Invention

[0005] To address the aforementioned issues in the prior art, the present invention aims to provide a distributed model-based predictive anti-interference control method for vehicle platoons that takes into account disturbance compensation using a distributed extended state observer. This method, based on an established time-delay dynamics model under an asynchronous sampling mechanism, enables real-time and accurate estimation and compensation control of a variety of uncertain disturbances, effectively improving the accuracy and stability of vehicle platoon control.

[0006] In order to achieve the above object, the technical solution of the present invention is as follows:

[0007] A distributed model predictive anti-interference control method for a vehicle platoon is disclosed. The method utilizes a distributed model predictive anti-interference control system for the vehicle platoon to perform control. The distributed model predictive anti-interference control system for the vehicle platoon is hereinafter referred to as the vehicle platoon control system. The disturbance compensation controller based on a distributed extended state observer is hereinafter referred to as the compensation controller.

[0008] The control method comprises the following steps:

[0009] Step 1: Initialization

[0010] The initialization module is responsible for checking the normal signal transmission and reception of the V2V communication module, perception module, mapping and localization module, decision-making and planning module, and actuators. It also loads the parameters of the following vehicle's longitudinal dynamics model, which includes an uncertain disturbance term, the asynchronous sampling mechanism based on random probability, the tracking error delay dynamics model parameters that account for random communication delays, the distributed model predictive controller parameters, and the compensation controller parameters. The decision-making and planning module, the upper-level module of the vehicle platoon control system, generates the desired speed and acceleration for the lead vehicle and instructs it to track these desired speeds and accelerations.

[0011] Step 2: Obtain the distributed model predictive controller objective function

[0012] According to the asynchronous sampling mechanism and the time-delay dynamics model, the objective function of the distributed model predictive controller is obtained.

[0013] Step 3: Obtain the nominal desired acceleration control law of the distributed model predictive controller based on the KKT condition method

[0014] Step 4: Obtain the uncertain disturbance value due to the unmodeled characteristics of the vehicle platoon control system

[0015] In order to estimate the uncertain disturbance caused by the unmodeled characteristics of the vehicle platoon control system, a distributed extended state observer is designed to estimate the total disturbance of each following vehicle in real time.

[0016] Step 5: Calculate the expected acceleration

[0017] Step 6: Perform distributed model predictive anti-disturbance control

[0018] For the expected acceleration u determined in step 5 i Control constraints are applied and filtered, and then sent as control signals to the following vehicle. The following vehicle's actuators perform distributed model predictive anti-interference control based on the final desired acceleration. Furthermore, a determination is made as to whether the following vehicle has achieved the control target. If so, the control task is completed; otherwise, the process proceeds to step 1.

[0019] Furthermore, the vehicle platoon control system, V2V communication module, mapping and positioning module, and decision-making and planning module are all installed in the controller of each vehicle, and the controller is connected to the perception module and actuator respectively through data cables.

[0020] Furthermore, the distributed model predictive anti-interference control system of the vehicle platoon includes an initialization module, a distributed model predictive controller and a disturbance compensation controller based on a distributed extended state observer.

[0021] The initialization module is responsible for checking whether the signal transmission and reception of the V2V communication module, perception module, mapping and positioning module, decision-making and planning module, and actuator are normal, loading the parameters of the longitudinal dynamics model of the following vehicle containing uncertain disturbance terms, loading the asynchronous sampling mechanism based on random probability, loading the parameters of the tracking error time-delay dynamics model considering random communication time delay, loading the parameters of the distributed model predictive controller, and loading the parameters of the compensation controller.

[0022] The distributed extended state observer (DESO) is composed of a linear DSO for the longitudinal kinematic model, enabling estimation of multiple uncertain disturbances. These uncertain disturbances are the sum of disturbances in the tracking process of the following vehicles in the platoon, including disturbances caused by the uncertainty of the unmodeled parts of the following vehicles in the platoon and disturbances caused by communication network delays under asynchronous sampling.

[0023] The distributed model predictive controller solves the quadratic programming problem based on the Karush-Kuhn-Tucker condition method (KKT condition method) to obtain the optimal nominal desired acceleration control law.

[0024] The compensation controller estimates the total uncertain disturbance of the vehicle platoon control system in real time and compensates the nominal control variable of the distributed model predictive controller. Ultimately, a desired acceleration control law is obtained by calculating the nominal desired acceleration of the distributed model predictive controller and the disturbance estimate of the compensation controller. This achieves the fusion of the distributed model predictive controller and the compensation controller to form a platoon distributed model predictive anti-interference control, completing closed-loop feedback and compensation adjustment.

[0025] Furthermore, the mathematical equation of the longitudinal dynamic model of the following vehicle containing the uncertain disturbance term in step 1 is as follows:

[0026]

[0027] Where i is the vehicle number of the following vehicle in the queue, i = {1, 2, ..., N}; p i (t) is the displacement of vehicle i; v i (t) is the speed of vehicle i; a i (t) is the acceleration of vehicle i; u i (t) is the control input vector; τ is the time constant; t is the current moment; f i (t) is the total disturbance; For p i The derivative of (t); v i The derivative of (t); for a i The derivative of (t).

[0028] Then construct the following state space equation:

[0029]

[0030] Where x i (t) is the state vector of the vehicle, x i (t)=[p i (t)v i (t)a i (t)] T ;u i (t) is the control input vector; y i (t) is the output vector; is x i The derivative of (t);

[0031]

[0032]

[0033] The state space equation is discretized using the zero-order hold method to obtain:

[0034]

[0035] Where, s is the integral variable with respect to time; T s is the sampling time, and k is the current moment after discretization.

[0036] Due to the uncertain disturbance f of the vehicle platoon control system i (t) is unknown, so the following nominal queue tracking model without disturbance terms is designed:

[0037]

[0038] Where x i (k) is the state vector of the vehicle, x i (k)=[p i (k)v i (k)a i (k)] T ;

[0039]

[0040] is the output vector; p0(k), v0(k) and a0(k) are the position, velocity and acceleration of the pilot car respectively; d des For the desired vehicle spacing, a fixed following distance is adopted, that is, the desired vehicle spacing is a constant d0.

[0041] First, an asynchronous sampling model that conforms to the random probability distribution is designed to simulate the phenomenon of random sampling in the actual signal. The sampling time at time k is T s,i Then, considering the influence of network time delay, during the kth sampling time, the control inputs at multiple moments will act on the current moment. The following time-delay dynamic model of the following vehicle is accurately constructed:

[0042]

[0043] Where, is the augmented state vector, is the output vector;

[0044]

[0045] Furthermore, the method for obtaining the objective function of the distributed model predictive controller in step 2 is as follows:

[0046] Set the prediction horizon N of each vehicle node controller p Same, control time domain N c Same, and satisfies N c ≤N p , then the state space equation in the prediction domain is as follows:

[0047]

[0048] Where:

[0049] X p,i (k) is the prediction time domain N p The state sequence under p,i (k) is the prediction time domain N pThe output state sequence under i (k) is the control time domain N c The input sequence below;

[0050]

[0051] U i (k)=[u i (k),u i (k+1),…,u i (k+N c -1)] T

[0052]

[0053]

[0054] Establishing an ideal exponential curve as a reference trajectory helps optimize the performance of the vehicle platoon control system, improve tracking accuracy and dynamic response capability, and the final distributed model predictive controller output target is The ideal curve established is as follows:

[0055]

[0056] Where α is a constant. Based on the established ideal curve, the ideal curve sequence is as follows:

[0057]

[0058] Where:

[0059]

[0060] Design the following standard quadratic programming problem:

[0061] minJ i =[U i T ΛU i +λ T ω λ λ]+ΘU i

[0062]

[0063] Where:

[0064] Λ=M E T QM E +R Nc

[0065] λ=[λ1λ2λ3λ4] T

[0066] ω λ =diag(ω λ1 ,ω λ2 ,ω λ3 ,ω λ4 )

[0067]

[0068] During the optimization process, it is necessary to constrain the state and control variables, so it is necessary to set upper and lower limits of hard constraints. At the same time, in order to avoid the controller being unable to solve due to overly strict constraints, a relaxation factor is introduced to soften the original constraints and set upper and lower limits of soft constraints. min ,Δv min ,Δa min ,u min are the hard constraints of spacing error, velocity error, acceleration error and control input, Δd max ,Δv max ,Δa max ,u max are the hard constraint upper limits of the spacing error, velocity error, acceleration error and control input respectively. In order to ensure the existence of a feasible solution in the optimization process, relaxation factors are introduced. λ1, λ2, λ3, and λ4 are the relaxation factors corresponding to the spacing error, velocity error, acceleration error and control input respectively. Δd min_s ,Δv min_s ,Δa min_s ,u min_s are the soft constraints of spacing error, velocity error, acceleration error and control input, Δd max_s ,Δv max_s ,Δa max_s ,u max_s are the soft constraint upper limits of spacing, velocity error, acceleration error and control input respectively.

[0069] Furthermore, the method for obtaining the nominal desired acceleration control law of the distributed model predictive controller based on the KKT condition method in step 3 is as follows:

[0070] The standard quadratic programming problem is transformed as follows:

[0071]

[0072] stA ζ ζ i ≤B ζ

[0073] Where:

[0074]

[0075] H=2diag(Λ,ω λ1 ,ω λ2 ,ω λ3 ,ω λ4 )

[0076] f i =[Θ i 0000] T

[0077]

[0078] Further differentiate the objective function J with respect to ζ to obtain:

[0079]

[0080] The stationary point ζ of the above formula * for:

[0081] ζ i * =-H -1 f i

[0082] From this we can determine the stationary point ζ * Whether the constraint A of the quadratic programming problem is satisfied ζ ζ i * ≤B ζ , if satisfied, then the optimal control sequence is ζ i * ,ζ i * The first element in is the nominal expected acceleration output by the distributed model predictive controller, which has the following formula:

[0083] u i * =ηζ i *

[0084] Where,

[0085] If the constraints of the quadratic programming are not met, the following Lagrangian function is constructed:

[0086]

[0087] where Q l is the identity matrix.

[0088] The Lagrangian function is further processed as follows:

[0089]

[0090] Where,

[0091] Then the objective function J l,i The stationary point ζ l,i The first value of is the nominal desired acceleration of the distributed model predictive controller:

[0092]

[0093] Where:

[0094]

[0095] O is a zero matrix.

[0096] Furthermore, in step 4, the uncertain disturbance value f caused by the unmodeled characteristics of the vehicle platoon control system is obtained. i The method of (t) is as follows:

[0097] First, the extended state observer of the longitudinal kinematic model is designed as follows:

[0098]

[0099] Where, f i [x 1,i (t),x 2,i (t)] is an unknown nonlinear function, w i (t) is the external disturbance, F i [x i (t),w i (t)]=f i [x 1,i (t),x 2,i (t)]+w i (t) is considered as an estimate of the total disturbance for each following vehicle, v i The derivative of (t), a des,i (t) is the expected acceleration of the i-th vehicle, u i (t) is the control input of the following vehicle i, f i (t) is the total disturbance of following vehicle i.

[0100] Let F i [x i (t),w i (t)] = x 3,i (t), The new state space equation is obtained as follows:

[0101]

[0102] Where, ξ i (t) = [x 1,i (t)x2,i (t)x 3,i (t)], B e =[01 / τ0], C e =

[001] .

[0103] To estimate the disturbance F of the vehicle platoon control system i [x i (t),w i (t)], design the following distributed extended state observer:

[0104]

[0105] Where, in x 1,i (t), x 2,i (t), x 3,i The observed value of (t), is the observer gain vector.

[0106] The discretized distributed extended state observer is as follows:

[0107]

[0108] Where T is the sampling time, That is the uncertain disturbance value f i (t) is an estimated value.

[0109] Furthermore, the method for calculating the expected acceleration in step 5 is as follows:

[0110] The real-time estimated value of the system uncertain disturbance calculated in step 4 is compensated in parallel to the nominal expected acceleration control law of the distributed model predictive controller, which is the final expected acceleration:

[0111]

[0112] Where, is the real-time estimated value of the system uncertainty disturbance of the i-th following vehicle.

[0113] Compared with the prior art, the present invention has the following beneficial effects:

[0114] 1. Based on the longitudinal dynamics model of the following vehicle containing uncertain disturbance terms, the present invention establishes a time-delay dynamics model under an asynchronous sampling mechanism that takes into account the communication network delay. The designed compensation controller can estimate in real time the uncertain disturbances caused by the following vehicle due to the unmodeled characteristics of the system, including but not limited to the uncertainty of the sampling time, the communication network delay and actuator delay, and the disturbance caused by the uncertainty of the vehicle model parameters. This improves the anti-interference ability of the queue controller, thereby enhancing the control accuracy, stability and robustness.

[0115] 2. The nominal control quantity of the distributed model predictive controller of the present invention is solved based on the KKT condition method, which provides a way to improve the real-time performance of the controller operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0116] Figure 1 It is a schematic diagram of the present invention.

[0117] Figure 2 Schematic diagram of the asynchronous sampling mechanism of the present invention.

[0118] Figure 3 It is a schematic diagram of the network communication time delay model of the present invention.

[0119] Figure 4 It is an implementation flow chart of the present invention. DETAILED DESCRIPTION

[0120] The following reference Figure 1-4 , the present invention is further described.

[0121] Figure 1 Shown is a schematic diagram of the present invention, which mainly consists of two parts:

[0122] (1) Distributed model predictive controller: The following vehicle i sends the vehicle position, velocity, and acceleration information to the longitudinal dynamics model that takes into account the system uncertainty disturbance. Under the asynchronous sampling mechanism, the state information of the pilot vehicle and the preceding vehicle is obtained according to the V2V communication method. At the same time, the controller network time-delay model is combined with the longitudinal dynamics model and sent to the time-delay dynamics model. Based on the time-delay dynamics model of the following vehicle, the distributed model predictive controller solves the quadratic programming problem based on the KKT condition method to obtain the nominal expected acceleration Asynchronous sampling mechanism based on random probability such as Figure 2 The controller network delay model is shown as Figure 3 shown.

[0123] (2) Disturbance compensation controller based on distributed extended state observer: The distributed extended state observer is composed of a linear extended state machine of the longitudinal kinematic model of the following vehicle. After receiving the position, velocity, and acceleration information of the following vehicle i and the nominal desired acceleration calculated by the distributed model predictive controller, the distributed extended state observer estimates the value of the following vehicle's uncertain disturbance and applies it as a compensation term together with the nominal desired acceleration to the longitudinal dynamic model of the following vehicle, thereby integrating the distributed model predictive controller and the compensation controller to form a distributed model predictive anti-interference control method for the platoon, and completing the closed-loop feedback and compensation adjustment of the platoon anti-interference control.

[0124] like Figure 1 As shown, the present invention uses a vehicle queue anti-interference control system for control. The design steps of the vehicle queue anti-interference control system are as follows:

[0125] Step 1: Design a longitudinal dynamic model of the following vehicle with uncertain disturbances

[0126] In order to achieve good control effect of vehicle platoon control system under uncertain disturbance, a longitudinal dynamic model of the following vehicle with uncertain disturbance is established, such as Figure 1 shown.

[0127] The longitudinal motion of the vehicle is affected by slope, air resistance, tire rolling resistance, and external uncertain disturbance factors. Therefore, the following longitudinal dynamic model is established:

[0128]

[0129] Where η T,i is the mechanical efficiency of the transmission system; r w,i is the tire radius; m i is the mass of the following vehicle i; is the equivalent air resistance; F f =m i gf i is the rolling resistance; F g =m i gsinθ is the slope resistance; F1 is the uncertainty disturbance caused by changes in the external environment; g is the acceleration of gravity; θ is the road slope; T i is the actual driving / braking torque of the vehicle; T des,i is the desired driving / braking torque of the vehicle.

[0130] The derivative of the velocity at the center of mass of the vehicle is approximately equal to the longitudinal acceleration of the vehicle, so we can get

[0131]

[0132] Where a i,Tis the acceleration generated by the vehicle's powertrain; a i,ex is the external acceleration, including rolling resistance acceleration, air resistance acceleration, and slope resistance acceleration; f 1,i is an uncertain disturbance.

[0133] To simplify the complexity of the model, the relationship between the expected acceleration and the actual acceleration can be approximated by a first-order transfer function:

[0134]

[0135] Where: f i (t) = f 1,i +f 2,i is the total disturbance, f 2,i is an unmodeled dynamic disturbance, assuming f i (t) is differentiable and Bounded. The above formula can be further expressed as:

[0136]

[0137] The longitudinal dynamic model with uncertain disturbances is obtained through discretization:

[0138]

[0139] Step 2: Establish a time-delay dynamics model under asynchronous sampling mechanism

[0140] The goal of vehicle platoon control is to keep the following vehicle at a desired distance from the preceding vehicle and track the speed of the lead vehicle, while also minimizing the acceleration of the following vehicle to ensure passenger comfort. That is,

[0141]

[0142] The present invention designs an asynchronous sampling model that conforms to the random probability distribution to simulate the phenomenon of random sampling in actual signals, such as Figure 2 The adjacent sampling times of the proposed asynchronous sampling model can be non-periodic and vary randomly, i.e., t k+1 -t k =h k ∈S, S={T1,T2,...,T n},0<T1<T2<…<T n Considering the above characteristics, for the i-th following vehicle (i={1,2,…,N}), the sampling time at time t is T s,i The event is but:

[0143]

[0144] Where, s=1,2,...,n,η s ∈[0,1] is a constant.

[0145] At time k, the time delay from the sensor to the controller is τ 1,i (k), the time delay of the controller output after solution is transmitted to the actuator through the CAN network is τ c,i (k), the time delay of the actuator is τ 2,i (k). Therefore, if Figure 3 As shown in Figure 2, the network delay of the vehicle platoon control system can be expressed as:

[0146] τ i (k) = τ 1,i (k)+τ c,i (k)+τ 2,i (k)

[0147] Assume that the time delay caused by the CAN network does not exceed the sampling time of the system and satisfies (τ 1,i (k)+τ c,i (k))∈(0,T s,i ). Furthermore, the upper bound of the network delay of the vehicle platoon control system can be defined as:

[0148]

[0149] Combined with the nominal platoon tracking model, the time-delay dynamic model of the vehicle platoon control system is obtained:

[0150]

[0151] Step 3: Design a distributed model predictive controller based on the KKT conditional method

[0152] Each vehicle node in the vehicle platoon control system is considered as a sub-prediction optimization problem. The prediction time domain N of each vehicle node controller is p and control time domain N c are the same and satisfy N c ≤N p , then the state space equation in the prediction domain is as follows:

[0153]

[0154] Establishing an ideal exponential curve as a reference trajectory helps optimize system performance, improve tracking accuracy and dynamic response capabilities, and the final controller output target is The ideal curve established is as follows:

[0155]

[0156] According to the established ideal curve, the ideal curve sequence can be obtained as follows:

[0157]

[0158] The objective function of the distributed model predictive controller is established as follows:

[0159]

[0160] Where, is the weight matrix of the output state quantity, is the weight matrix that controls the input quantity.

[0161] The distributed model predictive control problem is transformed into the following standard quadratic programming problem:

[0162] minJ i =[U i T ΛU i +λ T ω λ λ]+ΘU i

[0163]

[0164] The proposed quadratic programming problem can be transformed into the following form and then solved based on the KKT condition method:

[0165]

[0166] sA ζ ζ i ≤B ζ

[0167] Find the objective function J i The stationary point ζ * :

[0168]

[0169] make have to:

[0170] ζ i * =-H -1 f i

[0171] If the stationary point ζ * Satisfy constraint A ζ ζ i * ≤B ζ , then ζ i *The first element in is the nominal expected acceleration output by the distributed model predictive controller, so:

[0172] u i * =ηζ i *

[0173] If the constraint A is not satisfied ζ ζ i * ≤B ζ , then construct the following Lagrangian function:

[0174]

[0175] make Then we have:

[0176]

[0177] Then we get the stationary point ζ of the above formula l,i :

[0178]

[0179] ζ l,i The first element in is the nominal expected acceleration output by the distributed model predictive controller, which is expressed as follows:

[0180]

[0181] Step 4: Disturbance Compensation Controller Based on Distributed Extended State Observer

[0182] In order to estimate the uncertain disturbances caused by the unmodeled characteristics of the system, a distributed extended state observer is designed to estimate the total disturbance of each following vehicle in real time.

[0183] The linear extended state observer of the longitudinal kinematic model is designed as follows:

[0184]

[0185] The following state space equation is obtained:

[0186]

[0187] To estimate the disturbance F of the vehicle platoon control system i [x i (t),w i (t)], design the following distributed extended state observer:

[0188]

[0189] The discretized distributed extended state observer is as follows:

[0190]

[0191] The convergence analysis of the distributed extended state observer is as follows:

[0192] The estimation error of the distributed extended state observer is defined as η i (t) = [η 1,i (t)η 2,i (t)η 3,i (t)] T , observer gain vector Where ω0>0, When z=1,2,3, the differential equation for the estimation error can be obtained as follows:

[0193]

[0194] make It can be written as:

[0195]

[0196] Where H h is the Hurwitz matrix, L =

[001] T .

[0197] Assumption F i [x i (t),w i (t)] is bounded, there exists a constant σ z > 0 and a finite T1 > 0, so that z=1,2,3, for any t≥T1>0 and ω0>0. In addition, for a positive integer n,

[0198] Solution We can get:

[0199]

[0200] make:

[0201]

[0202] Because F i [x i (τ),w i (t)] is bounded, i.e. |F i [x i (τ),w i(t)]|≤δ, where δ is a positive constant, then for z=1,2,3, we have:

[0203]

[0204] For the definition of H h and L, as well as

[0205] in Because H h is a Hurwitz matrix, there exists a finite time T1>0 such that:

[0206]

[0207] For any t≥T1, z=1,2,3, n=1,2,3. Therefore:

[0208]

[0209] For any t≥T1, z=1,2,3. And T1 depends on ω0H h ,make:

[0210]

[0211] Then we have:

[0212]

[0213] For any t≥T1,z=1,2,3, You can get:

[0214]

[0215] For any t≥T1, z=1,2,3. Let η sum,i (0) = |η 1,i (0)|+|η 2,i (0)|+|η 3,i (0)|, then:

[0216]

[0217] For any t≥T1, z=1,2,3, the following holds:

[0218]

[0219] make according to And the above formula, we get:

[0220]

[0221] This holds true for any t ≥ T1, z = 1, 2, 3. It follows that the distributed extended state observer is bounded and convergent.

[0222] Step 5: Based on steps 3 and 4, the final expected acceleration is:

[0223]

[0224] Step 6: Apply control constraints and filter the final desired acceleration determined in Step 5. This is then sent as a control signal to the following vehicle. The following vehicle's execution module then performs distributed model predictive anti-interference control based on the final desired acceleration. Furthermore, the following vehicle is determined to have achieved the control target. If so, the vehicle completes the control task. Otherwise, steps 1 through 5 are repeated until the following vehicle stably achieves the platoon-following target and completes the control task.

[0225] The present invention is not limited to the details of the above embodiments. Any equivalent concepts or modifications within the technical scope disclosed by the present invention are included in the protection scope of the present invention.

Claims

1. A distributed model predictive anti-interference control method for a vehicle platoon, characterized by: Control is performed using a distributed model predictive anti-interference control system for vehicle platoons, the distributed model predictive anti-interference control system for vehicle platoons being referred to as a vehicle platoon control system, and the disturbance compensation controller based on a distributed extended state observer being referred to as a compensation controller. The control method comprises the following steps: Step 1: Initialization; The initialization module is responsible for checking whether the signal transmission and reception of the V2V communication module, perception module, mapping and positioning module, decision-making and planning module, and actuator are normal, loading the parameters of the longitudinal dynamics model of the following vehicle containing uncertain disturbance terms, loading the asynchronous sampling mechanism based on random probability, loading the parameters of the tracking error delay dynamics model considering random communication delay, loading the parameters of the distributed model predictive controller, and loading the parameters of the compensation controller. The decision-making and planning module is the upper module of the vehicle platoon control system. The decision-making and planning module generates the expected speed and acceleration of the leading vehicle and instructs the leading vehicle to track the expected speed and acceleration. Step 2: Obtain the distributed model predictive controller objective function; Obtaining a distributed model predictive controller objective function based on the asynchronous sampling mechanism and the time-delay dynamics model; Step 3: Obtain the nominal desired acceleration control law of the distributed model predictive controller based on the KKT condition method; Step 4: Obtain the uncertain disturbance value caused by the unmodeled characteristics of the vehicle platoon control system; In order to estimate the uncertain disturbance caused by the unmodeled characteristics of the vehicle platoon control system, a distributed extended state observer is designed to estimate the total disturbance of each following vehicle in real time. Step 5: Calculate the expected acceleration; Step 6: Perform distributed model predictive anti-disturbance control. For the expected acceleration u determined in step 5 i Control constraints are applied and filtered, and then sent as control signals to the following vehicle. The actuator of the following vehicle performs distributed model predictive anti-interference control on the following vehicle based on the final desired acceleration. Furthermore, it is determined whether the following vehicle has achieved the control target. If so, the control task is completed; otherwise, go to step 1.

2. The distributed model prediction anti-interference control method for a vehicle platoon according to claim 1, characterized in that: The vehicle platoon control system, V2V communication module, mapping and positioning module, and decision-making and planning module are all installed in the controller of each vehicle, and the controller is connected to the perception module and actuator respectively through data cables.

3. The distributed model prediction anti-interference control method for a vehicle platoon according to claim 1, characterized in that: The distributed model predictive anti-interference control system for the vehicle platoon includes an initialization module, a distributed model predictive controller and a disturbance compensation controller based on a distributed extended state observer; The initialization module is responsible for checking whether the signal transmission and reception of the V2V communication module, perception module, mapping and positioning module, decision and planning module, and actuator are normal, loading the parameters of the longitudinal dynamics model of the following vehicle containing uncertain disturbance terms, loading the asynchronous sampling mechanism based on random probability, loading the parameters of the tracking error time-delay dynamics model considering random communication time delay, loading the parameters of the distributed model predictive controller, and loading the parameters of the compensation controller; The distributed extended state observer is composed of a linear extended state observer of the longitudinal kinematic model, which estimates multiple uncertain disturbances. These multiple uncertain disturbances are the sum of disturbances in the process of following vehicles in the queue, including disturbances caused by the uncertainty of the unmodeled part of the following vehicles in the queue and disturbances caused by communication network delay under asynchronous sampling. The distributed model predictive controller solves the quadratic programming problem based on the Karush-Kuhn-Tucker condition method (KKT condition method) to obtain the optimal nominal desired acceleration control law; The compensation controller estimates the total uncertain disturbance of the vehicle platoon control system in real time and compensates the nominal control variable of the distributed model predictive controller. Ultimately, a desired acceleration control law is obtained by calculating the nominal desired acceleration of the distributed model predictive controller and the disturbance estimate of the compensation controller. This achieves the fusion of the distributed model predictive controller and the compensation controller to form a platoon distributed model predictive anti-interference control, completing closed-loop feedback and compensation adjustment.

4. The distributed model prediction anti-interference control method for a vehicle platoon according to claim 1, characterized in that: The mathematical equation of the longitudinal dynamic model of the following vehicle containing the uncertain disturbance term in step 1 is as follows: Where i is the vehicle number of the following vehicle in the queue, i = {1, 2, ..., N}; p i (t) is the displacement of vehicle i; v i (t) is the speed of vehicle i; a i (t) is the acceleration of vehicle i; u i (t) is the control input vector; τ is the time constant; t is the current moment; f i (t) is the total disturbance; For p i The derivative of (t); v i The derivative of (t); for a i The derivative of (t); Then construct the following state space equation: Where x i (t) is the state vector of the vehicle, x i (t)=[p i (t)v i (t)a i (t)] T ; u i (t) is the control input vector; y i (t) is the output vector; is x i The derivative of (t); The state space equation is discretized using the zero-order hold method to obtain: Where, s is the integral variable with respect to time; T s is the sampling time, k is the current moment after discretization; Due to the uncertain disturbance f of the vehicle platoon control system i (t) is unknown, so the following nominal queue tracking model without disturbance terms is designed: Where x i (k) is the state vector of the vehicle, x i (k)=[p i (k)v i (k)a i (k)] T ; is the output vector; p0(k), v0(k) and a0(k) are the position, velocity and acceleration of the pilot car respectively; d des The desired vehicle spacing is a fixed following distance, that is, the desired vehicle spacing is a constant d0; First, an asynchronous sampling model that conforms to the random probability distribution is designed to simulate the phenomenon of random sampling in the actual signal. The sampling time at time k is T s,i Then, considering the influence of network time delay, during the kth sampling time, the control inputs at multiple moments will act on the current moment; accurately construct the following time-delay dynamic model of the following vehicle: Where, is the augmented state vector, is the output vector; Γ i =τ i (k-m)-T s,i (k-m)-T s,i (k-m+1)-...-T s,i (k-1) 5. The distributed model prediction anti-interference control method for a vehicle platoon according to claim 1, characterized in that: The method for obtaining the objective function of the distributed model predictive controller described in step 2 is as follows: Set the prediction horizon N of each vehicle node controller p Same, control time domain N c Same, and satisfies N c ≤N p , then the state space equation in the prediction domain is as follows: Where: X p,i (k) is the prediction time domain N p The state sequence under p,i (k) is the prediction time domain N p The output state sequence under i (k) is the control time domain N c The input sequence below; YOU i (k)=[u i (k),u i (k+1),…,u i (k+N c -1)] T Establishing an ideal exponential curve as a reference trajectory helps optimize the performance of the vehicle platoon control system, improve tracking accuracy and dynamic response capability, and the final distributed model predictive controller output target is The ideal curve established is as follows: Where α is a constant; the ideal curve sequence obtained based on the established ideal curve is as follows: Where: Design the following standard quadratic programming problem: Where: λ=[λ1λ2λ3λ4] T oh λ =diag(ω λ1 ,oh λ2 ,oh λ3 ,oh λ4 ) In the optimization process, the state and control variables need to be constrained, so the upper and lower limits of the hard constraints need to be set. At the same time, in order to avoid the controller being unable to solve due to overly strict constraints, the relaxation factor is introduced to soften the original constraints and set the upper and lower limits of the soft constraints; Δd min ,Δv min ,Δa min ,u min are the hard constraints of spacing error, velocity error, acceleration error and control input, Δd max ,Δv max ,Δa max ,u max are the hard constraint upper limits of the spacing error, velocity error, acceleration error and control input respectively. In order to ensure the existence of a feasible solution in the optimization process, relaxation factors are introduced. λ1, λ2, λ3, and λ4 are the relaxation factors corresponding to the spacing error, velocity error, acceleration error and control input respectively. Δd min_s ,Δv min_s ,Δa min_s ,u min_s are the soft constraints of spacing error, velocity error, acceleration error and control input, Δd max_s ,Δv max_s ,Δa max_s ,u max_s are the soft constraint upper limits of spacing, velocity error, acceleration error and control input respectively.

6. The distributed model prediction anti-interference control method for a vehicle platoon according to claim 1, characterized in that: The method for obtaining the nominal expected acceleration control law of the distributed model predictive controller based on the KKT condition method in step 3 is as follows: The standard quadratic programming problem is transformed as follows: stA ζ g i ≤B ζ Where: H=2diag(Λ,ω) λ1 ,oh λ2 ,oh λ3 ,oh λ4 ) f i =[Θ i 0 0 0 0] T Further differentiate the objective function J with respect to ζ to obtain: The stationary point ζ of the above formula * for: From this we can determine the stationary point ζ * Whether the constraints of the quadratic programming problem are met If it satisfies, the optimal control sequence is The first element in is the nominal expected acceleration output by the distributed model predictive controller, which has the following formula: Where, If the constraints of the quadratic programming are not met, the following Lagrangian function is constructed: where Q l is the identity matrix; The Lagrangian function is further processed as follows: Where, Then the objective function J l,i The stationary point ζ l,i The first value of is the nominal desired acceleration of the distributed model predictive controller: Where: O is a zero matrix.

7. The distributed model prediction anti-interference control method for a vehicle platoon according to claim 1, characterized in that: The method for obtaining the uncertain disturbance value caused by the unmodeled characteristics of the vehicle platoon control system described in step 4 is as follows: First, the extended state observer of the longitudinal kinematic model is designed as follows: Where, f i [x 1,i (t),x 2,i (t)] is an unknown nonlinear function, w i (t) is the external disturbance, F i [x i (t),w i (t)]=f i [x 1,i (t),x 2,i (t)]+w i (t) is considered as an estimate of the total disturbance for each following vehicle, v i The derivative of (t), a des,i (t) is the expected acceleration of the i-th vehicle, u i (t) is the control input of the following vehicle i, f i (t) is the total disturbance of following vehicle i; Let F i [x i (t),w i (t)] = x 3,i (t), The new state space equation is obtained as follows: Where, ξ i (t) = [x 1,i (t)x 2,i (t)x 3,i (t)], B e =[01 / τ0], C e =[001]; To estimate the disturbance F of the vehicle platoon control system i [x i (t),w i (t)], design the following distributed extended state observer: Where, in x 1,i (t), x 2,i (t), x 3,i The observed value of (t), is the observer gain vector; The discretized distributed extended state observer is as follows: Where T is the sampling time, That is the uncertain disturbance value f i (t) is an estimated value.

8. The distributed model prediction anti-interference control method for a vehicle platoon according to claim 1, characterized in that: The method for calculating the expected acceleration described in step 5 is as follows: The real-time estimated value of the system uncertain disturbance calculated in step 4 is compensated in parallel to the nominal expected acceleration control law of the distributed model predictive controller, which is the final expected acceleration: Where, is the real-time estimated value of the system uncertainty disturbance of the i-th following vehicle.

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