A connected vehicle cooperative control method based on adaptive feedback technology

Abstract

This invention provides a connected vehicle cooperative control method based on adaptive feedback technology, comprising the following steps: establishing a simplified vehicle queuing control model; acquiring the actual control input of each following vehicle while considering controller gain variations; adding an adaptive feedback controller; optimizing the adaptive feedback controller to calculate tracking error while considering packet loss in inter-vehicle communication data; and transforming the vehicle queuing control model to achieve vehicle queuing control. This invention proposes a distributed adaptive feedback controller for vehicle queuing that guarantees both internal stability and L2 queue stability, wherein the feedback gain and parameter adaptive law of each following vehicle are dynamically determined based on its own tracking error. This avoids the packet loss matrix mentioned earlier, significantly reducing computational complexity.

Description

Technical Field

[0001] This invention relates to the technical field of cooperative control methods, and more particularly to a cooperative control method for connected vehicles based on adaptive feedback technology. Background Technology

[0002] Many urban roads and highways are currently facing serious problems such as traffic congestion, high fuel consumption, severe air pollution, and frequent traffic accidents [1-2]. Connected vehicle cooperative control technology can enable vehicles entering the road to automatically platoon, thereby improving road efficiency. On the one hand, vehicles can maintain a small distance between each other, thereby reducing air resistance and achieving energy conservation and emission reduction; on the other hand, unmanned driving technology can effectively improve road traffic safety. Using vehicle wireless communication technology [3-4], vehicles can share position, speed, and acceleration information to ensure the internal stability and platoon stability of the vehicle platoon system. Currently, the lead vehicle-navigator following (LPF) is a commonly used communication topology in vehicle platoon control [5]. Under this topology, all following vehicles can obtain the navigator's status information. Vehicle Ad Hoc Networks (VANETs) have limited bandwidth and a large number of vehicle nodes communicating through them [6]. As a result, vehicle platooning control systems often face many communication constraints, such as communication delay [7], data packet loss [8-9], quantization effects

[10] , and media access constraints [11-12].

[0003] Existing studies [7-12], [14-16] typically assume that the control law calculated by the vehicle queuing controller is precisely executed at the actuator end of the vehicle. However, this assumption does not hold true in practical applications, mainly for the following reasons

[17] : (i) the word length of the control command is limited; (ii) the parameters need to be fine-tuned before execution; and (iii) the aging and failure of the actuator, which leads to changes in controller gain and perturbations. The perturbation of the vehicle controller gain and the influence of communication limitations will reduce the performance of vehicle queuing control. Therefore, it is necessary to design a vehicle queuing control method that can overcome the influence of communication limitations and controller gain perturbations at the same time. To this end, this paper is based on the communication topology of lead vehicle-navigator following (LPF) and adopts a constant distance (CS) vehicle spacing strategy to consider the packet loss effect and unknown variable gain controller perturbation in heterogeneous vehicle queuing control problem. An adaptive controller is introduced to estimate and compensate for the unknown controller gain perturbation. Through stability analysis of the established uncertain adaptive switching control system, the design method of the vehicle's adaptive feedback controller is given.

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[31] QianS, GangT.Adaptivecontrolofpiecewiselinearsystems:Theoutputtrackingcase[C] / / AmericanControlConference.IEEE, 2010. Summary of the Invention

[0037] In view of the technical problems mentioned in the background section, a cooperative control method for connected vehicles based on adaptive feedback technology is provided.

[0038] The technical means employed in this invention are as follows:

[0039] A cooperative control method for connected vehicles based on adaptive feedback technology includes the following steps:

[0040] Step 1: Establish a simplified vehicle queuing control model;

[0041] Step 2: Taking into account the controller gain variation, obtain the actual control input for each following vehicle;

[0042] Step 3: Add an adaptive feedback controller; Step 3, the added adaptive feedback controller further includes the following steps:

[0043] Step 31: Set the step size γ iσ Set initial values ​​so that the matrix is ​​in P iσ If ≥0 exists, the inequality has a feasible solution;

[0044] Step 32: Based on a certain step size γ iσ Increase Δγ iσ ;

[0045] Step 33: If the matrix is ​​in P iσ If it is feasible when >0 exists, then return to step 32; otherwise, go to step 34 and set γ. iσ =γ iσ -Δγiσ ;

[0046] Step 34: For the obtained maximum γ iσ Choose an initial μ i Make the matrix in P iσ It is feasible if >0 exists;

[0047] Step 35: Based on a certain step size Δμ i Decrease μ i ;

[0048] Step 36: Check the feasibility of inequalities (26)-(28); if feasible, return to step 35; otherwise, go to step 37 and set μ. i =μ i +Δμ i ;

[0049] Step 37: For the obtained maximum γ iσ and minimum μ i The obtained matrix P iσ Determine the adaptive feedback (10);

[0050] Step 4: To calculate the tracking error, optimize the adaptive feedback controller considering packet loss in workshop communication data;

[0051] Step 5: Transform the vehicle platoon control model to achieve vehicle platoon control.

[0052] Compared with the prior art, the present invention has the following advantages:

[0053] 1) This invention proposes a method that can guarantee both internal stability and... The vehicle queue distributed adaptive feedback controller for queue stability is used, in which the feedback gain and parameter adaptive law of each following vehicle are dynamically determined based on its own tracking error. This avoids the packet loss matrix mentioned in [8] and significantly reduces the computational complexity.

[0054] 2) This invention employs adaptive switching control technology to handle unknown gain changes in the vehicle queuing control system, while ensuring zero tracking error and... Queue stability. Using adaptive estimation laws to handle these problems can avoid distinguishing different types of controller gain perturbations

[17] and dealing with complex inequalities

[18] during the controller design process.

[0055] 3) This invention establishes the workshop data packet loss rate, controller gain perturbation range, and... The relationship between queue stability is presented, and the convergence rate and maximum allowable packet loss rate involved are given in analytical form. Attached Figure Description

[0056] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0057] Figure 1 This is a schematic diagram illustrating the key factors involved in the heterogeneous vehicle queue control of this invention.

[0058] Figure 2 This is a schematic diagram of the adaptive feedback controller of the present invention.

[0059] Figure 3 This represents the state of data packet loss during vehicle-to-vehicle communication in this invention.

[0060] Figure 4 The control performance of a heterogeneous vehicle fleet using the proposed adaptive feedback controller in this invention is as follows: (a) spacing error; (b) speed error; (c) speed; (d) acceleration.

[0061] Figure 5 This is an adaptive feedback controller for each follower in this invention.

[0062] Figure 6 To improve the control performance of the heterogeneous queue with a pure feedback controller, the present invention provides u i (t)=u i k (t): (a) vehicle spacing error; (b) speed error; (c) speed; (d) acceleration. Detailed Implementation

[0063] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0064] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0065] like Figure 1-6 As shown, this invention provides a network vehicle cooperative control method based on adaptive feedback technology. The goal of vehicle platoon control is to achieve speed tracking of the following vehicle to the leader vehicle and control of the vehicle spacing, while satisfying the internal stability requirements of tracking control and the platoon stability requirements

[19] . There are two types of vehicle platoons: one is a homogeneous vehicle platoon, in which the vehicles have the same dynamic model and parameters, and the other is a heterogeneous vehicle platoon (see Figure 1 For vehicle platooning control systems, key factors include vehicle dynamics, control strategy, communication issues, and spacing strategy

[14] (see Figure 1 Constant spacing (CS) and variable spacing are typical spacing strategies used in vehicle platooning control. Another important issue in vehicle platooning systems is the communication topology. Common communication topologies include: forward following (PF), bidirectional PF (BPF), and LPF.

[0066] Based on vehicular ad hoc networks, consider a heterogeneous vehicle queue consisting of N+1 vehicles traveling on a horizontal road (see...). Figure 1 ). Using z i v i a i Let represent the position, velocity, and acceleration of the i-th vehicle, where i = 0, 1, ..., N. The lead vehicle periodically sends its velocity v0 and acceleration a0 to each following vehicle via an onboard ad hoc network. Each following vehicle is equipped with an onboard distance sensor to measure its distance from the vehicle in front. The communication between vehicles uses a typical LPF communication topology.

[0067] A cooperative control method for connected vehicles based on adaptive feedback technology, characterized by the following steps:

[0068] Step 1: Establish a simplified vehicle queuing control model; To simplify the vehicle queuing control model, the following assumptions are made:

[0069] 1) The longitudinal slippage of the tires can be ignored, and the dynamic characteristics of the vehicle's power system can be described by a first-order inertial element.

[0070] 2) The vehicle itself has a rigid structure and is symmetrical.

[0071] 3) The effects of the vehicle's pitch and yaw motions can be ignored.

[0072] 4) The driving and braking torques are controllable.

[0073] Based on the above assumptions, this invention presents a simplified nonlinear dynamic model.

[0074]

[0075] Where m i It is the quality of the vehicle, C A,i It is the combined aerodynamic drag coefficient, g is the acceleration due to gravity, and f is the combined aerodynamic drag coefficient. i It is the rolling resistance coefficient, T i T represents the actual driving / braking torque. i,des This represents the control input, i.e., the required drive / brake torque. It is the inertial delay of vehicle dynamics, R i Indicates the tire radius. It refers to the mechanical efficiency of the transmission system. The acceleration 'a' is... i (t) Differentiate with respect to time and derive the required driving / braking torque using the inverse model

[13] -

[15] .

[0076]

[0077] This involves precise feedback linearization techniques, u i The auxiliary control input to be designed is given. Substituting equation (2) into equation (1), the nonlinear vehicle model can be rewritten as the following third-order nonlinear vehicle dynamic model, and used for the analysis and design of the controller.

[0078]

[0079] Because of each car The following vehicles may differ, therefore heterogeneous dynamic responses of the vehicles are considered. To ensure that the following vehicle maintains a constant distance and desired speed from the lead vehicle, the vehicle tracking error (i.e., the distance error δ) is defined. i (t) , velocity error and acceleration error They are respectively:

[0080]

[0081] Where d > 0 represents the desired distance between two continuously following vehicles, and a lateral spacing strategy is adopted. Taking the derivative of the tracking error defined in (4) with respect to time, we can obtain...

[0082]

[0083] make and Let represent the tracking error vector and the output vector, respectively. According to equation (5), the expression for the tracking error system is:

[0084]

[0085] C =

[010] and This is the disturbance term. Here, the velocity error is... This is considered interference primarily because adjacent vehicles in a convoy are dynamically coupled, so a sudden change in the speed of the vehicle in front can affect the tracking error of the following vehicle. This phenomenon not only affects the stability of the convoy but also impacts passenger comfort and can even lead to rear-end collisions.

[0086] like Figure 2 As shown, the controller u of each following vehicle i (t) also includes the following feedback controller based on tracking error:

[0087]

[0088] in This is the gain of the steady-state feedback controller to be determined. Data packet loss is unavoidable during vehicle communication (e.g., ...). Figure 2 The open / closed-loop system in the controller (7) affects the tracking performance of the controller (7). Therefore, the definition is... This is used to calculate the tracking error vector for the control input of each following vehicle. and These represent the velocity error and acceleration error used to calculate the control input, respectively. Here, we introduce... To reflect the impact of packet loss on the defined tracking error vector e i The effect of (t).

[0089] Step 2: Taking into account the controller gain variation, obtain the actual control input for each following vehicle; In feedback control based on tracking error, the variation of controller gain is unavoidable for the following reasons: (1) the controller parameters may change due to saturation and quantization during implementation

[25] ; (2) the actual values ​​of the component parameters in the control equipment may change abruptly due to aging, external stress damage or adverse weather conditions [1]. As described in

[17] ,

[18] ,

[26] , taking into account the effect of controller gain variation, the actual control input for each following vehicle is:

[0090]

[0091] in It's about feedback controllers. controller gain K i Unknown gain perturbation.

[0092] Assumption 1: ΔK i It has known upper and lower bounds, for example and

[0093] Step 3: Add an adaptive feedback controller; Models that handle controller gain perturbations are generally classified into two categories: product uncertainty

[17] and summation uncertainty

[18] . Existing research mainly focuses on

[0094] simple The purpose of a state feedback controller is to make the controller insensitive to changes in gain. The state feedback controller designed by Yang et al.

[17] and Haddade et al. is a typical example. It should be noted that the designed controller depends on the type of controller gain change. On the one hand, complex norm bounded inequalities are required for different gain perturbations. On the other hand, it is impractical to distinguish controller gain perturbations in actual fleet control systems because they are usually unknown. Since adaptive control is a typical method for dealing with uncertain systems, an adaptive estimation law is introduced to estimate and compensate for the changes in gain caused by ΔK. i The resulting interference. Therefore, in the controller u i Add the following adaptive controller to (t).

[0095]

[0096] in It is an estimate ΔK for unknown gain perturbation. i Combined with feedback controller and adaptive controller The following adaptive feedback controller is derived:

[0097]

[0098] To calculate the tracking error defined in (4), each following vehicle must obtain the speed information v0(t) and acceleration information a0(t) of the lead vehicle through the onboard ad hoc network. Since packet loss is unavoidable, a switching signal σ(t)∈{c,o} is introduced to describe the state of packet loss. Specifically, if the data packet transmission is successful, the system is in a closed-loop state σ(t)=c, then v0(t) and a0(t) can be used by the i-th following vehicle to calculate the vehicle tracking error, i.e. and When packet loss occurs, the loop is opened, σ(t) = 0, and the zeroing strategy [9],

[12] is used to define and Based on the above discussion, the tracking error vector is summarized.

[0099]

[0100] The corresponding matrix and They are respectively

[0101]

[0102] Considering the impact of packet loss, design the following adaptive feedback controller u with switching mechanism. i (t).

[0103]

[0104] The details are as follows:

[0105]

[0106] The symbols "c" and "o" represent closed-loop and open-loop control modes, respectively.

[0107] In step 3, the added adaptive feedback controller also includes the following steps:

[0108] Step 31: Set the step size γ iσ Set initial values ​​so that the matrix is ​​in P iσ If ≥0 exists, the inequality has a feasible solution;

[0109] Step 32: Based on a certain step size γ iσ Increase Δγ iσ ;

[0110] Step 33: If the matrix is ​​in P iσ If it is feasible when >0 exists, then return to step 32; otherwise, go to step 34 and set γ. iσ=γ iσ -Δγ iσ ;

[0111] Step 34: For the obtained maximum γ iσ Choose an initial μ i Make the matrix in P iσ It is feasible if >0 exists;

[0112] Step 35: Based on a certain step size Δμ i Decrease μ i ;

[0113] Step 36: Check the feasibility of inequalities (26)-(28); if feasible, return to step 35; otherwise, go to step 37 and set μ. i =μ i +Δμ i ;

[0114] Step 37: For the obtained maximum γ iσ and minimum μ i The obtained matrix P iσ Determine the adaptive feedback (10);

[0115] Step 4: To calculate the tracking error, optimize the adaptive feedback controller considering packet loss in workshop communication data;

[0116] Step 5: Transform the vehicle platoon control model to achieve vehicle platoon control. Switch controller (12) to establish a tracking error system for each following vehicle in the platoon. Switch controller u... i Substituting (t) into (8), the actual control input u for each following vehicle is... i ′(t) is expressed by the following formula

[0117]

[0118] Define the parameter estimation error as

[0119] The control input can then be re-expressed as

[0120]

[0121] Substituting the control input (14) into (6), the tracking error of the following vehicle i is:

[0122]

[0123] Among them, A iσ(t) =A i -B i K iσ(t) ,K iσ(t) =Ki Π σ(t) and and and Let σ(t) ∈ {c, o}, and let matrix A be the equivalent controller gain and parameter estimation error in the switching control system, respectively. io The characteristic polynomial is

[0124]

[0125] Since the aforementioned characteristic polynomial lacks a corresponding term for the operator s, according to the Routh-Herwitz stability criterion, matrix A i -B i K io It is unstable, that is, the queuing system in open-loop mode is unstable. The purpose of this study is to establish an adaptive feedback control strategy (10) for vehicle queuing to meet the following conditions:

[0126] 1) The vehicle platoon is internally stable, ensuring that following vehicles can track the speed of the lead vehicle and maintain the desired inter-vehicle distance, i.e.

[0127]

[0128] Assuming the acceleration of the lead car is zero or constant, that is... The stability of the queue is defined as follows:

[0129] Definition 1

[13] : A vehicle platoon with linear time-invariant dynamics has internal stability if and only if its closed-loop control system is asymptotically stable.

[0130] 2) The vehicle platoon satisfies the following conditions under zero initial tracking error: Requirements for queue stability.

[0131] Each subsystem of the switching queue tracking error system (15) is a special case of the following cascaded state-space system.

[19]

[0132]

[0133] The following definition queue stability

[0134] Definition 2

[19] : ( Queue stability) Consideration (15) of the exchange interconnection queue control system Let be the set of tracking error vectors. This represents the vector corresponding to u0 = 0 in (15). If there exists a function of type u0 = 0... and any Such that for any initial tracking error, the following conditions are met. And for any If true, then system (15) satisfies Queue stability.

[0135]

[0136] In addition, when The current style also holds true

[0137]

[0138] Lemma1: Consider a connected vehicle platooning control system. The system obeys a strict observable if and only if the following condition is met and the controller u0 = 0 has zero initial tracking error: Queue stability.

[0139]

[0140] Wherein, parameter γ d This reflects the attenuation effect of speed error along the vehicle platoon.

[0141] Proof: Condition (20) can be easily obtained by using a proof criterion similar to that of Lemma 1 in

[19] .

[0142] Definition 1:

[27] For any t2>t1≥0, let N i (t1,t2) represents the number of times σ(t) switches on [t1,t2]. If N i (t1,t2)≤N0+(t2-t1) / T ia For T ia If T > 0 and N0 ≥ 0 holds true, then T is called T. ia Let N0 be the average dwell time and N0 be the oscillation boundary. In general, let N0 = 0.

[0143] For ease of analysis and discussion, define the following quantity: Let T i -(t) represents the total activation time of the following vehicle i within the time interval [t0,t) when the switch signal satisfies σ(t)=0. This is known as packet loss rate.

[0144] To meet the internal stability requirements of vehicle platooning control (16) and Queue stability (20) requirement. To stabilize the tracking error and parameter estimation error, a piecewise Lyapunov function (15) is defined for each sub-mode of the system tracking error as follows.

[0145]

[0146] In the formula, the symbol σ∈{c,o}, and the matrix and Note the derivative V of the Lyapunov equation as defined. iσ (t) differs depending on whether the model is open-loop or closed-loop; therefore, the following lemma is provided to characterize V. iσ The derivative of (t) has certain properties.

[0147] Lemma2: For the adaptive feedback controller (10), if the adaptive estimation law is designed as follows:

[0148]

[0149] Then the Lyapunov function V defined in (21) iσ (t) satisfies

[0150] in:

[0151] γ ic >0, γ io <0, and matrix P iσ Satisfying the following matrix inequalities

[0152]

[0153] Proof: Please see Appendix A for details.

[0154] According to the average dwell time technique

[28] , when the average dwell time of each mode is large enough and the total working time of the unstable mode is relatively small compared with the stable mode, the stability of the switching queue control system (15) can be guaranteed. Combined with Lemma 2, the main results of the stability of the queue switching tracking error system (15) are given.

[0155] Theorem 1: Consider the queue switching tracking error system (15). For a given scalar γ ic >0, γ io <0, μ i >1, 0<γ d ≤1, and S i >0, if the upper limit of packet loss rate is

[0156]

[0157] And the matrix has P iσ >0 The following inequalities exist

[0158]

[0159]

[0160] P ic ≤μ iP io ,P io ≤μ i P ic (28)

[0161]

[0162] With the defined positive constant ξ i To maintain consistency, and then satisfy the condition under zero initial conditions using an adaptive feedback controller (10). Queue stability. The feedback controller gain and the estimated adaptive law are designed by (30) and (22), respectively.

[0163]

[0164] Example 1

[0165] The effectiveness of the proposed control method was verified by numerical experiments. For this purpose, a realistic and simplified nonlinear vehicle dynamics model (1) was used in the simulation. The parameter values ​​of the nonlinear vehicle dynamics (1) were randomly selected according to the bus listed in Table 1

[15] .

[0166] The acceleration a0(t) of the lead car is set as follows:

[0167]

[0168] Table I: Nonlinear Vehicle Dynamics Parameters

[0169]

[0170] Table II: Parameters in the controller solution

[0171]

[0172] First, Algorithm 1 is used to determine the proposed adaptive feedback controller. Table II provides the corresponding parameters during the solution process. Feasibility Matrix Pic and Pio As shown in Table III. Using the data given in Table IV, the maximum allowable packet loss rate r can be calculated. i * =47.82%. Therefore, the obtained matrices can be used separately. Pic and Pio To determine the feedback controller gain and adaptive estimation law, the gain matrix of the proposed adaptive controller is given here. Si and the obtained feedback gain Ki They are Si=diag{1,1,1}, K1=[1.51 1.69 1.73], K2=[1.35 1.50 1.80], K3=[1.34 1.83 1.62] and K4=[1.55 1.68 1.93].

[0173] Next, in the experiment, we consider controller gain perturbation

[17] , such as ΔK i =[k ij (δ K1 +δ K2 )] 1×3 , where δ K1 and δ K2 Is it satisfied by |δ K1 |=|δ K2 |≤1 is an indeterminate parameter of the constraint

[17] . For unreliable inter-vehicle communication, its data packet loss is as follows Figure 3 Specifically, when the y-axis value is "1", it indicates that the velocity v0 and acceleration a0 can be successfully transmitted to the following vehicle i; otherwise, its value is "0". Table IV gives the relevant packet loss rate r for each following vehicle. i and average length of stay T ia Clearly, all the conditions in Theorem 1 are satisfied.

[0174] Third, the control performance of the vehicle platoon was analyzed using the designed adaptive feedback controller. In the simulation, the initial tracking error of each follower was set to δ. i (t) = 0 and from Figure 4 The tracking performance shown demonstrates that the designed adaptive feedback controller can guarantee stable tracking error of the queue under varying controller gain and packet loss conditions. Within the time range [0, 20 s], observations were made... Figure 4 The tracking error oscillates because the acceleration given in (38) is disturbed, causing the speed of each following vehicle to change. Since the speed error does not increase with the number of vehicles (see...), Figure 4 (b)) is therefore satisfied. Queue stability requirements. Figure 5 The control input quickly becomes zero, which means that the proposed parameter estimation law helps compensate for unknown controller gain variations. These figures demonstrate that the proposed control algorithm is effective. Figure 6 The control results for a vehicle platoon without the adaptive controller are shown. Figure 4 and Figure 6 In comparison, it was found Figure 6 The overshoot of the tracking error is significantly greater than Figure 4 The overshoot in the data. For example... Figure 6The maximum spacing error of the queues in (a) is significantly greater than Figure 4 (a).

[0175] Table III: Feasibility Matrix P ic and P io

[0176]

[0177] Proof of Theorem 1

[0178] Theorem 1 holds only if the following conditions are met:

[0179] 1) When ω i (t)≡0, ensuring internal stability.

[0180] 2) When the initial tracking error is 0, the following inequality is satisfied:

[0181]

[0182] First, it needs to be proven that when ω i When (t)≡0, the system remains stable internally. According to Lemma 2, V iσ(t) (t) is relative to a continuous time interval where the two ends of the time interval are discontinuous (e.g., t∈[t]). k ,t k+1 The time derivative of )) is

[0183]

[0184] Add a constraint γ to both ends of B2. iσ(t) C′ i ,get

[0185]

[0186] Since t∈[t k ,t k+1 ),σ(t)=c, according to formula (B3), we get

[0187]

[0188] Since t∈[t k ,t k+1 )$,$σ(t)=c is obtained according to formula (B3)

[0189]

[0190] In the above formula, the conclusion from reference

[31] is used. Next, we can find a constant ξ. ic >0 satisfies:

[0191]

[0192] Similarly, for t∈[t k-1 ,t k From $, $σ(t)=o, we can obtain

[0193]

[0194] This would result in a constant -1 < ξ. io <0, thus making the following equation true.

[0195]

[0196] It is important to note at this point that the piecewise Lyapunov function V... iσ(t) (t), t∈[t k ,t k+1 The value of V affects its convergence speed. iσ(t) (t) Based on formulas (B5) and (B7), it is necessary to analyze V. iσ(t) (t) in each switching time interval [t k ,t k+1 Different situations:

[0197] Case 1: For time intervals t∈[t] k ,t k+1 Lyapunov function V iσ(t) The value of (t) is not increasing, that is,

[0198] Case 2: For time intervals t∈[t k-1 ,t k Lyapunov function V iσ(t) The value of (t) is not decreasing, that is,

[0199]

[0200] Combining Case 1 and Case 2, within the time interval [t0, t], t k+1 >t>t k >...>t1>t0, k≥1 can be obtained

[0201]

[0202] Multivalued functions The definition is given in formula (33). Due to the tracking error e i (t) and parameter estimation error They are all continuous, and we get and in It is the switching moment. Using condition (28) in Theorem 1, we get...

[0203]

[0204] Connect formulas (B8) and (B9)

[0205]

[0206] Further derivation using formula (B10) leads to...

[0207]

[0208] in

[0209]

[0210] and

[0211]

[0212] By analyzing the function in formula (33) The definition is obtained.

[0213]

[0214] In order to find V iσ(t) The upper limit of (t) is analyzed. In the following cases within the time interval [t0,t].

[0215] Case 1: During each switching time interval, the Lyapunov function V iσ The value of (t) remains unchanged at this time.

[0216]

[0217] Case 2: Lyapunov function V iσ Increasing or decreasing the value of (t) will cause

[0218]

[0219] Where ξ i It is a positive number and satisfies

[0220]

[0221] get

[0222]

[0223] Based on the average residence time in Definition 1, we obtain

[0224]

[0225] Meanwhile, by using the condition of average residence time (29), we obtain

[0226]

[0227] Based on the upper limit of packet loss rate given in condition (25), it is guaranteed that

[0228] γ ic (1-r i )+γ io r i ≥0 (B21)

[0229] This means ρ i ≤0.

[0230] Case 3: Lyapunov function V iσ The value of (t) is variable in some switching time intervals and invariant in others. In this case, Based on the analysis of Case 1 and 2, we obtain

[0231]

[0232] Where ρ i ∈( ρ i ,0).

[0233] Based on (21) and (32), we can obtain

[0234]

[0235] Based on the above analysis, the estimated value of the tracking error in formula (31) can be derived. According to formula (31), we can obtain... Using Barbalatˉs lemma in reference

[30] , we can analyze and obtain e i (t) will asymptotically converge to zero, therefore when ω i When (t)≡0, the internal stability proposed in (16) is proved.

[0236] The above analysis provides a proof for condition 2). For time intervals [t0, t], t k+1 >t>t k >...>t1>t0, k≥1, according to formula (23) in Lemma 2, the Lyapunov function V iσ(t) (t) needs to satisfy

[0237]

[0238] Combining formulas (B11) and (B24) yields

[0239]

[0240] Under the condition that the initial tracking error is zero, the analysis formula (B25) yields...

[0241]

[0242] Based on the proof of Theorem 1, Analysis of values, derivation

[0243]

[0244] Integrating both sides of inequality (B27) from t = t0 to t = ∞ yields inequality (B1). Therefore, the requirement for queue stability is satisfied.

[0245] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments. In the above embodiments of the present invention, the descriptions of each embodiment have their own emphasis; parts not described in detail in a certain embodiment can be referred to in the relevant descriptions of other embodiments. It should be understood that the disclosed technical content in the several embodiments provided in this application can be implemented in other ways.

[0246] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for cooperative control of connected vehicles based on adaptive feedback technology, characterized in that, Includes the following steps: S1: Establish a simplified vehicle queuing control model; S2: Consider the controller gain variation to obtain the actual control input for each following vehicle; S3: Add an adaptive feedback controller, including the following steps: S31: Set step size The initial value is set so that the matrix is in There exists a feasible solution for the inequality under the condition that S32: according to a certain step length increase ; S33: If the matrix is feasible under the constraints, return to S32; otherwise, go to S34, set ; S34: For the obtained maximum , select one initial such that the matrix is feasible under the constraints. S35: according to a certain step size reducing ; S36: check the feasibility of inequalities (26)-(28); if feasible, go back to S35; otherwise go to S37 and set ; S37: For the obtained maximum , minimum , matrix determine adaptive feedback (10); S4: To calculate the tracking error, optimize the adaptive feedback controller considering packet loss in workshop communication data; S5: Transform the vehicle platoon control model to achieve vehicle platoon control; In S3, a piecewise Lyapunov function (15) is defined for each sub-mode of the system tracking error as follows: (21)； symbol ,matrix and The derivative of the defined Lyapunov equation The differences lie between open-loop and closed-loop models; therefore, the following lemma is provided to characterize them. The derivative properties; For the adaptive feedback controller (10), if the estimation law is: (21)； Lyapunov function defined in (21) satisfies (23); , , , and matrix satisfy the following matrix inequalities: (24)； Based on the average dwell time technique, when the average dwell time of each mode is large enough and the total working time of the unstable mode is relatively small compared with the stable mode, the stability of the switching queue control system (15) is guaranteed, and the main results of the stability of the queue switching tracking error system (15) are given. Consider a queue switching tracking error system (15); given a scalar , , , , and if the packet loss rate upper bound is: (25)； matrix exists the following inequalities exist （26）； （27）； (28)； (29)； with the defined normal number In keeping with the above, the adaptive feedback controller (10) is used to satisfy Queue stability; feedback controller gain and estimation adaptive law are given by (30) and (22), respectively: (30) When the internal stability of the system is guaranteed, giving an estimate of the tracking error: (31) when , (32) wherein , . 2.The cooperative control method for connected vehicles based on adaptive feedback technology according to claim 1, wherein, In S1, to simplify the vehicle platooning control model, the following assumptions are made: 1) Tire longitudinal slippage is negligible, and the dynamic characteristics of the vehicle's power system are described using a first-order inertial element; 2) The vehicle itself meets the requirements of a rigid structure and is symmetrical; 3) The effects of the vehicle's pitch and yaw motions are negligible; 4) The driving and braking torques are controlled.

3. The cooperative control method for connected vehicles based on adaptive feedback technology according to claim 1 or 2, characterized in that, The simplified nonlinear dynamic model is as follows: (1)； in, Indicates the mass of the vehicle. This represents the combined aerodynamic drag coefficient. Represents gravitational acceleration. Indicates the rolling resistance coefficient. Indicates the actual driving / braking torque. This represents the control input, i.e., the required drive / brake torque. Indicates the inertial delay in vehicle dynamics. Indicates the tire radius. Indicates the mechanical efficiency of the transmission system; expresses acceleration. Differentiating with respect to time, the required driving / braking torque is derived using an inverse model: (2)； wherein, denotes the auxiliary control input; substituting equation (2) into equation (1), the nonlinear vehicle model is rewritten into the following third-order nonlinear vehicle dynamic model, which is used for the analysis and design of the controller; (3)； Because of each car Since the following vehicles can differ from the lead vehicle, their heterogeneous dynamic responses are taken into account. To ensure that the following vehicle maintains a constant distance and desired speed from the lead vehicle, the vehicle tracking error, i.e., the distance error, is defined. Speed ​​error and acceleration error They are respectively: (4)； where, denotes the desired distance between two consecutive following vehicles and the lateral distance strategy is adopted; taking the derivative of the tracking error defined in (4) with respect to time, we have: (5)； Let and denote the tracking error vector and the output vector, respectively; the expression of the tracking error system is given by equation (5) as follows: （6）； and It is a disturbance term. 4.The cooperative control method for connected vehicles based on adaptive feedback technology according to claim 1, wherein, In step S2, considering the controller gain variation, the actual control input of each following vehicle is obtained; the actual control input of each following vehicle is: (8)； wherein, is an unknown gain perturbation of the controller gain of the feedback controller ​ 5. The cooperative control method of connected vehicles based on adaptive feedback technology according to claim 1, characterized in that, The controller added in S3 is: (9) wherein, denotes an estimate for the unknown gain perturbation in combination with a feedback controller and an adaptive controller , an adaptive feedback controller is derived as follows: (10)。 6.The cooperative control method for connected vehicles based on adaptive feedback technique according to claim 1, wherein, The controller added in S5 is: The switching controller The actual control input (8) for each following vehicle is then brought in Is expressed by the equation (13)； The parameter estimation error is defined as The control input is then represented as (14)； Substituting control input (14) into (6) will result in the following vehicle. The tracking error is (15)； where and ; and and , respectively, denote the equivalent controller gain and parameter estimation error in the switching control system; the notation By calculation, the characteristic polynomial of the matrix is ； Due to the missing corresponding term of the operator in the above characteristic polynomial, the matrix is unstable according to the Routh-Hurwitz stability criterion, i.e. the queue system in open loop mode is unstable.

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