A preset time vehicle cooperative control method with preset transient state performance

Abstract

The application provides a preset time vehicle cooperative control method with preset transient state performance, and relates to the technical field of vehicle cooperative control. The method specifically comprises the following steps: constructing a vehicle fleet and establishing a vehicle model containing model uncertainty for all vehicles in the vehicle fleet except the head vehicle; adopting a leader-follower formation strategy to establish a queue relationship between the vehicles under the constraints of relative distance and relative direction angle between the vehicles; designing a preset time cooperative controller of the vehicle based on a preset time observer and a control signal to complete the design of the preset time cooperative controller of the vehicle based on the preset time observer for all vehicles in the vehicle fleet except the head vehicle. The preset time vehicle cooperative control based on the preset transient state performance is realized, that is, the vehicle communication connectivity is ensured and the collision between the vehicles is avoided while achieving the queue movement target.

Description

Technical Field

[0001] This invention relates to the field of vehicle cooperative control technology, and in particular to a preset-time vehicle cooperative control method with preset instantaneous steady-state performance. Background Technology

[0002] Vehicle cooperative control, as an important branch of intelligent transportation systems, has received much attention in recent years. To achieve cooperative vehicle control, maintaining individual vehicle stability, communication connectivity within the vehicle platoon, and preventing collisions between platoons are essential. The communication connectivity of the vehicle platoon and the prevention of collisions can be considered as a vehicle spacing constraint problem. Currently, researchers have proposed many effective control methods to address this problem. Among them, the paper "Adaptive sliding mode control of vehicular platoons with prescribed tracking performance" published in 2019 IEEE Transactions on Vehicular Technology (pp. 7511-7520) utilizes a transformation function to convert constrained vehicle spacing into unconstrained vehicle spacing; and the paper "BLF-based neutral fault-tolerant control for nonlinear vehicular platoon with time-varying fault directions and distance restrictions" published in 2021 IEEE Transactions on Intelligent Transportation Systems (pp. 12388-12398) introduces a barrier Lyapunov function to implement vehicle spacing constraints. However, the above methods only consider one-dimensional longitudinal vehicle models that are limited in practical application scenarios, which cannot meet the needs of practical applications. Therefore, the paper "Distributed neuroadaptive fault-tolerant sliding-mode control for 2-D planevehicular platoon systems with spacing constraints and unknown directionfaults" published in Automatica 2021 (page 109675) discusses the vehicle cooperative control problem in a two-dimensional plane for two-dimensional vehicle models. However, the vehicle cooperative error controlled in this paper is asymptotically convergent, while in practical applications, the convergence speed of the controller is required to be high.The paper "Event-triggered multi-lane fusion control for 2-D vehicle platoon systems with distance constraints", published in 2023 IEEE Transactions on Intelligent Vehicles (pages 1498-1511), proposes a fixed-time vehicle cooperative controller based on the fixed-time lemma. However, due to the complexity of the expression for the convergence time, it is difficult to predetermine the required upper limit of the convergence time for this fixed-time scheme.

[0003] In summary, current research on vehicle cooperative control largely focuses on one-dimensional unidirectional control, with limited research on two-dimensional vehicle platoons. Furthermore, existing research on two-dimensional vehicle platoons is mostly finite-time or fixed-time control, meaning the convergence time expression is a complex function, making it difficult to predefine the required upper limit of convergence time. In addition, some existing methods do not consider the uncertainties in vehicle modeling. Summary of the Invention

[0004] To address the shortcomings of the existing technologies, this invention proposes a preset-time cooperative controller based on a preset-time observer that guarantees specified transient and steady-state performance. This method provides a preset-time vehicle cooperative control method with preset transient and steady-state performance, which achieves the queuing movement target while ensuring vehicle communication connectivity and avoiding collisions between vehicles.

[0005] The present invention proposes a preset-time vehicle cooperative control method with preset instantaneous steady-state performance, comprising the following steps:

[0006] Step 1: Construct a convoy of N+1 vehicles and determine the first vehicle in the convoy as the lead vehicle. For all vehicles in the convoy except the lead vehicle, establish a vehicle model containing model uncertainties.

[0007] Step 2: Adopt the leader-following formation strategy to establish the queue relationship between vehicles under the constraints of relative distance and relative direction angle;

[0008] Step 3: Design a preset time observer for the i-th vehicle;

[0009] Step 4: Design the control signal for the i-th vehicle, and together with the preset time observer of the i-th vehicle, form the preset time cooperative controller for the i-th vehicle based on the preset time observer;

[0010] Step 5: Take i = 2, 3, ..., N+1 in sequence, and repeat steps 3-4 in sequence until the design of the preset time cooperative controller based on the preset time observer for all vehicles in the convoy except the lead vehicle is completed, so as to realize the preset time vehicle cooperative control that guarantees the preset instantaneous steady-state performance.

[0011] Furthermore, for the i-th vehicle in the convoy, where i = 2, 3, ..., N+1, the vehicle model containing the model uncertainty term is established as follows:

[0012]

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019] Where x c,i It is the x-coordinate position of the i-th vehicle in the inertial coordinate system; It is x c,i The derivative of y; c,i It is the position of the i-th vehicle in the inertial coordinate system; It is y c,i The derivative of θ i It is the deflection angle of the i-th vehicle relative to the horizontal direction; It is θ i The derivative of v; c,i Is the i-th car at θ i Linear velocity in the direction; It is v c,i The derivative of; w c,i It is the angular velocity of the i-th vehicle; It is w c,i The derivative; a v,i It is the linear acceleration of the i-th vehicle; It is a v,i The derivative; a w,i It is the angular acceleration of the i-th vehicle; It is a w,i The derivative of u; v,i It is the accelerator or brake input control signal for the i-th vehicle; u w,i It is the steering wheel input control signal for the i-th vehicle; m i τ is the mass of the i-th vehicle; iF is the engine time constant of the i-th vehicle; U,i This is the modeling uncertainty for the i-th vehicle;

[0020] Furthermore, step 2 also includes:

[0021] A leader-follower formation strategy is adopted, and a directed graph with a directed spanning tree is used to describe the communication relationship between vehicles. The convoy consisting of N+1 vehicles is decomposed into N subsystems consisting of a leader vehicle and a follower vehicle. The lead vehicle in the convoy follows a preset trajectory and is regarded as the root of the directed spanning tree of the directed graph.

[0022] Step 2, the process of establishing the queue relationship between the vehicles, includes:

[0023] Define any pair of vehicles accompanying a leader. Assume the j-th vehicle in the convoy is the leader's vehicle, and the i-th vehicle is the follower's vehicle, where i∈{2,...,N+1}, j∈{1,2,...,N+1}, and i≠j. Then the relative distance d between the leader's vehicle and the follower's vehicle is... c,i and relative direction angle for:

[0024]

[0025]

[0026] Where x c,j y is the x-coordinate of the j-th vehicle in the inertial coordinate system; c,j It is the position of the j-th vehicle in the inertial coordinate system;

[0027] To ensure communication connectivity between vehicles, the relative distance constraints and relative orientation angle constraints between vehicles are set as follows:

[0028]

[0029]

[0030] Where t represents time; d c,con,i It is the maximum ranging value of the on-board sensor of the i-th vehicle, and satisfies 0. <d c,con,i ; It is the maximum measured orientation angle value of the on-board sensor of the i-th vehicle, and satisfies d c,con,i and The value depends on the measurement and sensing capabilities of the vehicle communication equipment;

[0031] To prevent collisions between adjacent vehicles, the relative distance constraints between vehicles are further set as follows:

[0032]

[0033] Where d c,col,i The pre-set safe distance between vehicles, and satisfying 0 <d c,col,i <d c,con,i ;

[0034] Define vehicle cooperation errors, including: distance cooperation error and angle cooperation error;

[0035] e cd,i =d c,i -d c,des,i (13)

[0036]

[0037] Where e cd,i It is distance cooperation error; It is the angular cooperation error; d c,des,i The desired relative distance is set, and it satisfies 0. <d c,col,i <d c,des,i <d c,con,i ; The desired relative direction angle is set, and it satisfies...

[0038] The performance function is used to constrain the collaborative error boundary:

[0039]

[0040]

[0041] in k cd,i , All are performance functions to be given, and satisfy...

[0042] Furthermore, the design of the preset time observer for the i-th vehicle includes: the observed values ​​of the preset time observer. First derivative Represented as:

[0043]

[0044] in,

[0045]

[0046]

[0047]

[0048]

[0049] Where s i It is an auxiliary variable; It is s i The derivative; f i and S i All are intermediate variables; yes The derivative; α d These are design parameters, and they satisfy 0 < α. d <1;t d,S and t d,s Both are time parameters to be given, and t d,S >0, t d,s >0;k S and k η These are design parameters, and k η ≥0, k S Satisfying inequalities in The modeling uncertainty F for the i-th vehicle U,i The first derivative, The modeling uncertainty F for the i-th vehicle U,i first derivative model The upper bound;

[0050] Furthermore, the control signals in step 4 include: virtual control signals, accelerator or brake input control signals, and steering wheel input control signals;

[0051] Step 4, which involves constructing the preset time cooperative controller for the i-th vehicle based on a preset time observer, includes: designing the virtual control signals for the i-th vehicle:

[0052]

[0053]

[0054] α i,2 =q m (φ mi,2 -ψ m z i,2 )+(1-q m )(φ mi,2 (30)

[0055]

[0056] Design the accelerator or brake input control signal for the i-th vehicle:

[0057] u v,i =q m mi τ i (φ mi,3 -ψ m z i,3 )+(1-q m )m i τ i (φ mi,3 (32)

[0058] Design the steering wheel input control signal for the i-th vehicle:

[0059]

[0060] in,

[0061] z i,2 =v c,i -α i,1 (34)

[0062] z i,3 =a v,i -α i,2 (35)

[0063]

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[0065]

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[0088] Where α i,1 α i,2 , All of these are virtual control signals for the i-th vehicle; It is α i,1 The derivative; It is α i,2 The derivative; yes The derivative; yes The derivative of z; i,2 z i,3 , α i,1 , q m ψ m , φ mi,1 , L mi,1 , κ mi , φ mi,2 φ mi,3 , All are intermediate variables; t f It is the preset time parameter of the preset time cooperative controller of the i-th vehicle based on the preset time observer, and t f The preset time of the observer is greater than the preset time. η m , k1, k, k2, k3 The given design parameters are both positive, and p is a positive integer, satisfying the inequality 2p≥3; θ j It is the deflection angle of the j-th vehicle relative to the horizontal direction; v c,j Is the j-th car at θ? j Linear velocity in the direction; It is d c,des,i The derivative; yes k cd,i The derivative; yes The derivative; yes The derivative; yes The derivative; yes The derivative of .

[0089] The beneficial effects of adopting the above technical solution are as follows:

[0090] This invention addresses the cooperative control problem of multi-vehicle systems with modeling uncertainties. It proposes a preset-time vehicle cooperative control method with preset instantaneous steady-state performance. This method designs a preset-time observer that can accurately estimate unknown modeling uncertainties within a preset time. The preset-time observer can effectively compensate for a series of effects brought about by modeling uncertainties during the control design process, making the system more robust and adaptable while enhancing the controllability of the observation speed.

[0091] The present invention takes into account the limitations of the capabilities of on-board communication equipment during vehicle platooning and the safety requirement to avoid collisions between vehicles. It pre-sets the transient and steady-state performance of the vehicles and designs a preset time cooperative controller based on a preset time observer that can guarantee the specified transient and steady-state performance. This enables the cooperative movement of vehicles to be achieved within a preset time while ensuring vehicle communication connectivity and avoiding collisions.

[0092] Compared to one-dimensional unidirectional vehicle queues, the method of this invention considers two-dimensional vehicle queues with modeling uncertainties, making it more general and universal for practical applications. Attached Figure Description

[0093] Figure 1 This is a flowchart of a preset time vehicle cooperative control method with preset instantaneous steady-state performance in this embodiment;

[0094] Figure 2 This is a schematic diagram illustrating the basic setup of a pair of leader-following vehicles in the leader-following formation strategy of this embodiment.

[0095] Figure 3This is a schematic diagram of the vehicle platoon's travel trajectory in this embodiment;

[0096] Figure 4 This is a schematic diagram of the observation error of the second vehicle in this embodiment;

[0097] Figure 5 This is a schematic diagram illustrating the observation error of the observer for the third vehicle in this embodiment;

[0098] Figure 6 This is a schematic diagram of the distance cooperation error and the corresponding performance function of the second vehicle in this embodiment;

[0099] Figure 7 This is a schematic diagram of the angular cooperation error of the second vehicle and the corresponding performance function in this embodiment;

[0100] Figure 8 This is a schematic diagram of the distance cooperation error and corresponding performance function of the third vehicle in this embodiment;

[0101] Figure 9 This is a schematic diagram of the angular cooperation error of the third vehicle and the corresponding performance function in this embodiment. Detailed Implementation

[0102] To facilitate understanding of this application, specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and embodiments. The following embodiments are illustrative of the invention but are not intended to limit its scope. Rather, these embodiments are provided to provide a more thorough and complete understanding of the disclosure of this application.

[0103] This embodiment provides a preset-time vehicle cooperative control method with preset instantaneous steady-state performance, such as... Figure 1 As shown, it includes the following steps:

[0104] Step 1: Construct a convoy of N+1 vehicles and determine the first vehicle in the convoy as the lead vehicle. For all vehicles in the convoy except the lead vehicle, establish a vehicle model containing model uncertainties.

[0105] For the i-th vehicle in the convoy, where i = 2, 3, ..., N+1, the vehicle model containing the model uncertainty term is established as follows:

[0106]

[0107]

[0108]

[0109]

[0110]

[0111]

[0112]

[0113] Where x c,i It is the x-coordinate position of the i-th vehicle in the inertial coordinate system; It is x c,i The derivative of y; c,i It is the position of the i-th vehicle in the inertial coordinate system; It is y c,i The derivative of θ i It is the deflection angle of the i-th vehicle relative to the horizontal direction; It is θ i The derivative of v; c,i Is the i-th car at θ i Linear velocity in the direction; It is v c,i The derivative of; w c,i It is the angular velocity of the i-th vehicle; It is w c,i The derivative; a v,i It is the linear acceleration of the i-th vehicle; It is a v,i The derivative; a w,i It is the angular acceleration of the i-th vehicle; It is a w,i The derivative of u; v,i It is the accelerator or brake input control signal for the i-th vehicle; u w,i It is the steering wheel input control signal for the i-th vehicle; m i τ is the mass of the i-th vehicle; i F is the engine time constant of the i-th vehicle; U,i This is the modeling uncertainty for the i-th vehicle;

[0114] Step 2: Adopt a leader-following formation strategy to establish the queue relationship between vehicles under the constraints of relative distance and relative direction angle;

[0115] A leader-follower formation strategy is adopted, and a directed graph with a directed spanning tree is used to describe the communication relationship between vehicles. The convoy consisting of N+1 vehicles is decomposed into N subsystems consisting of a leader vehicle and a follower vehicle. The lead vehicle in the convoy follows a preset trajectory and is regarded as the root of the directed spanning tree of the directed graph.

[0116] In this implementation, it is assumed that the convoy consists of N+1 vehicles, where the lead vehicle does not require control and automatically travels along an ideal trajectory, while the remaining N vehicles require control. A leader-follower relationship is established in the leader-follower convoy strategy, such as... Figure 2 As shown, j represents the j-th vehicle in the convoy, j∈{1,2,...,N+1}; in this convoy, the lead vehicle can only act as the leader vehicle, while the other vehicles can act as both follower and leader vehicles; therefore Figure 2 Assume that the j-th and i-th vehicles in the convoy form a subsystem consisting of a lead vehicle and a follower vehicle. In this case, the j-th vehicle is the lead vehicle, the i-th vehicle is the follower vehicle, and i ≠ j. The relative distance d between them is... c,i and relative direction angle Also there Figure 2 The bid was successful.

[0117] The process of establishing the queue relationship between the vehicles includes:

[0118] Define any pair of vehicles accompanying a leader. Assume the j-th vehicle in the convoy is the leader's vehicle, and the i-th vehicle is the follower's vehicle, where i∈{2,...,N+1}, j∈{1,2,...,N+1}, and i≠j. Then the relative distance d between the leader's vehicle and the follower's vehicle is... c,i and relative direction angle for:

[0119]

[0120]

[0121] Where x c,j y is the x-coordinate of the j-th vehicle in the inertial coordinate system; c,j It is the position of the j-th vehicle in the inertial coordinate system;

[0122] To ensure communication connectivity between vehicles, the relative distance constraints and relative orientation angle constraints between vehicles are set as follows:

[0123]

[0124]

[0125] Where t represents time; d c,con,i It is the maximum ranging value of the on-board sensor of the i-th vehicle, and satisfies 0. <d c,con,i ; It is the maximum measured orientation angle value of the on-board sensor of the i-th vehicle, and satisfies d c,con,i and The value depends on the measurement and sensing capabilities of the vehicle communication equipment;

[0126] To prevent collisions between adjacent vehicles, the relative distance constraints between vehicles are further set as follows:

[0127]

[0128] Where d c,col,i The pre-set safe distance between vehicles, and satisfying 0 <d c,col,i <d c,con,i ;

[0129] Define vehicle cooperation errors, including: distance cooperation error and angle cooperation error;

[0130] e cd,i =d c,i -d c,des,i (13)

[0131]

[0132] Where e cd,i It is distance cooperation error; It is the angular cooperation error; d c,des,i The desired relative distance is set, and it satisfies 0. <d c,col,i <d c,des,i <d c,con,i ; The desired relative direction angle is set, and it satisfies...

[0133] The performance function is used to constrain the collaborative error boundary:

[0134]

[0135]

[0136] in k cd,i , All are performance functions to be given, and satisfy...

[0137] In this embodiment, the following assumptions are made:

[0138] 1) Modeling uncertainty F of the i-th vehicle U,i It is an unknown and bounded time-varying function, and its first derivative is... satisfy in, It is an upper bound on the modulus of the first derivative of the modeling uncertainty term for the i-th vehicle, and It is a positive number;

[0139] 2) Assume that the initial time t0 of the convoy is 0, i.e. t0 = 0, and that the initial state of the vehicles in the convoy does not violate the set constraints, i.e., formulas (10) to (12).

[0140] Under assumptions 1) to 2), a preset time cooperative controller based on a preset time observer is designed to enable cooperative movement of vehicles within a preset time while ensuring vehicle communication connectivity and avoiding collisions.

[0141] Step 3: Design a preset time observer for the i-th vehicle;

[0142] The preset time observer for the i-th vehicle includes: the observed values ​​of the preset time observer. First derivative Represented as:

[0143]

[0144] in,

[0145]

[0146]

[0147]

[0148]

[0149] Where s i It is an auxiliary variable; It is s i The derivative; f i and S i All are intermediate variables; yes The derivative; α d These are design parameters, and they satisfy 0 < α. d <1;t d,S and t d,s Both are time parameters to be given, and t d,S >0, t d,s >0;k S and k η These are design parameters, and k η ≥0, k S Satisfying inequalities in The modeling uncertainty F for the i-th vehicle U,i The first derivative;

[0150] In fact, it is not necessary to know the modeling uncertainty F of the i-th vehicle. U,i Upper bound of the modulus of the first derivative The specific value only needs to satisfy the design parameter k. S The value is greater than That's all.

[0151] To prove the stability of the designed pre-defined time observer, a pre-defined time lemma is first given: Consider the system If there exists a continuous function V with parameter 0 < α < 1 and convergence time T > 0, such that the inequality... Established, If the derivative of a continuous function V is given, then the system... It is time-stable and has an upper bound on its convergence time.

[0152] Define observation error

[0153]

[0154] Differentiating equation (18) and substituting the resulting equations (6), (19), and (20) into equation (21) yields:

[0155]

[0156] Constructing Lyapunov functions:

[0157]

[0158] Differentiating formula (24) with respect to time, we get:

[0159]

[0160] in It is V S,i The derivative; It is S i The derivative;

[0161] According to the preset time lemma, at the preset time... If the intermediate variable S i If it converges to 0, then it indicates an observation error. The observer converges to 0 within a preset time, meaning it converges to 0 within the preset time. Internally accurate estimation of unknown modeling uncertainties.

[0162] When S i When =0, then according to formula (21) we get Now, we construct a new Lyapunov function:

[0163]

[0164] Differentiating formula (26) with respect to time, we get:

[0165]

[0166] in It is V s,i The derivative;

[0167] According to the lemma of preset time, it can be obtained that at the preset time... Internal, auxiliary variable s i Converging to 0;

[0168] In summary, when at the preset time Internal, intermediate variable S i Converging to 0, and within a preset time. Internal, auxiliary variable s i Converging to 0 indicates that the designed observer is time-stable.

[0169] Step 4: Design the control signal for the i-th vehicle, and together with the preset time observer of the i-th vehicle, form the preset time cooperative controller for the i-th vehicle based on the preset time observer.

[0170] The control signals include: virtual control signals, accelerator or brake input control signals, and steering wheel input control signals;

[0171] The process of constructing the preset time cooperative controller for the i-th vehicle based on the preset time observer includes:

[0172] Design the virtual control signal for the i-th vehicle:

[0173]

[0174]

[0175] α i,2 =q m (φ mi,2 -ψ m z i,2 )+(1-q m )(φ mi,2 (30)

[0176]

[0177] Design the accelerator or brake input control signal for the i-th vehicle:

[0178] u v,i =q m m i τ i (φ mi,3 -ψ m z i,3)+(1-q m )m i τ i (φ mi,3 (32)

[0179] Design the steering wheel input control signal for the i-th vehicle:

[0180]

[0181] in,

[0182] z i,2 =v c,i -α i,1 (34)

[0183] z i,3 =a v,i -α i,2 (35)

[0184]

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[0200]

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[0209] Where α i,1 α i,2 , These are all virtual control signals for the i-th vehicle; It is α i,1 The derivative; It is α i,2 The derivative; yes The derivative; yes The derivative of z; i,2 z i,3 , α i,1 , q m ψ m , φ mi,1 , L mi,1 , κ mi , φ mi,2 φ mi,3 , All are intermediate variables; t f It is the preset time parameter of the preset time cooperative controller of the i-th vehicle based on the preset time observer, and t f The preset time of the observer is greater than the preset time. η m , k1, k, k2, k3 θ are both positive design parameters to be given, where p is a positive integer and satisfies the inequality 2p≥3; jIt is the deflection angle of the j-th vehicle relative to the horizontal direction; v c,j Is the j-th car at θ? j Linear velocity in the direction; It is d c,des,i The derivative; yes k cd,i The derivative; yes The derivative; yes The derivative; yes The derivative; yes The derivative;

[0210] In this embodiment, a stability analysis is performed on the designed preset time cooperative controller based on a preset time observer, that is, the preset time cooperative controller based on a preset time observer is divided into two parts: a distance cooperative controller and an angle cooperative controller based on a preset time observer, and the stability analysis is performed on them.

[0211] Prove the stability of the distance cooperative controller based on a preset time observer:

[0212] Construct the Lyapunov function with respect to distance as follows:

[0213]

[0214] Based on the designed preset time observer, virtual control signal, throttle or brake input control signal of the i-th vehicle, and performance function (formula 15), let t0 be the initial time, take t0 = 0, and when t0 ≤ t <t f When the constructed Lyapunov function with respect to distance is differentiated with respect to time, we get:

[0215]

[0216] in It is V cd,i The derivative of (t); and thus we can obtain Integrating both sides of it with respect to time t from 0 to t, we get: Therefore, we can obtain Right now Solving but Therefore, we can obtain Therefore

[0217] When t≥t f At that time, one can obtain And V cd,i (t f) = 0, that is: when t ≥ t f At that time, V cd i(t) = 0 Therefore e cd,i =0, z i,2 =0, z i,3 =0; that is, at the preset time t f Within this range, the distance cooperation error converges to 0 and remains stable, and the preset instantaneous steady-state performance is guaranteed.

[0218] Similarly, prove the stability of the angle cooperative controller;

[0219] Construct the Lyapunov function with respect to angle:

[0220]

[0221] Based on the virtual control signal, the steering wheel input control signal of the i-th vehicle, and the performance function, i.e., formula (16), when t0≤t <t f When the constructed Lyapunov function with respect to angle is differentiated with respect to time, we get:

[0222]

[0223] in yes The derivative; and thus we can obtain Integrating both sides of it with respect to time t from 0 to t, we get: Therefore, we can obtain Right now Solving but Therefore, we can obtain Therefore

[0224] When t≥t f At that time, one can obtain and That is: when t≥t f hour, Therefore That is, at the preset time t f Within the range, the angle cooperation error converges to 0 and remains stable, and the preset instantaneous steady-state performance is guaranteed.

[0225] In summary, both the distance coordination error and the angle coordination error of the vehicles can be resolved within a preset time t. f The preset time cooperative controller for the i-th vehicle, based on the preset time observer, converges to zero and is preset time stable.

[0226] Step 5: Take i = 2, 3, ..., N+1 in sequence, and repeat steps 3-4 in sequence until the design of the preset time cooperative controller based on the preset time observer for all vehicles in the convoy except the lead vehicle is completed, so as to realize the preset time vehicle cooperative control that guarantees the preset instantaneous steady-state performance.

[0227] In this embodiment, a vehicle platoon consisting of three vehicles is used as an example to verify the effectiveness of the above control method. The simulation software used in this embodiment is MATLAB, and the simulation description is as follows:

[0228] This implementation considers a vehicle convoy consisting of three vehicles, divided into two subsystems: one consisting of the first vehicle and the second vehicle, and the other consisting of the second vehicle and the third vehicle. In the first vehicle and the second vehicle subsystem, the first vehicle is the leader vehicle and the second vehicle is the follower vehicle, i.e., j=1, i=2; in the second vehicle and the third vehicle subsystem, the second vehicle is the leader vehicle and the third vehicle is the follower vehicle, i.e., j=2, i=3. Now, considering the uncertainty in vehicle modeling, a preset-time vehicle cooperation controller based on a preset-time observer is designed to ensure that the vehicle cooperation error converges within a preset time, while maintaining vehicle communication connectivity and avoiding collisions between vehicles.

[0229] Let the masses of the first, second, and third vehicles be m1 = m2 = m3 = 1607 kg, and the engine time constants of the first, second, and third vehicles be τ2 = τ3 = 0.25. Assume the expressions for the unknown modeling uncertainties of the second and third vehicles are: The initial state is defined as (x) c,1 (0),y c,1 (0),θ1(0),v c,1 (0),w c,1 (0),a v,1 (0),a w,1 The linear acceleration of the first car (0) = (0,0,π / 4,0,0,0,0) is 0.5 m / s². 2 , where x c,1 (0) is the x-coordinate of the first vehicle in the inertial coordinate system at the initial moment, y c,1 (0) is the position of the first vehicle in the inertial coordinate system at the initial moment, θ1(0) is the deflection angle of the first vehicle relative to the horizontal direction at the initial moment, and v c,1 (0) is the linear velocity of the first vehicle in the direction θ1(0) at the initial moment, w c,1 (0) is the angular velocity of the first vehicle at the initial moment, a v,1 (0) is the linear acceleration of the first vehicle at the initial moment, a w,1(0) is the angular acceleration of the first vehicle at the initial moment. Let the initial states of the second and third vehicles be: (x c,3 (0),y c,3 (0),θ3(0),v c,3 (0),w c,3 (0),a v,3 (0),a w,3 (0))=(-3.1,-3,0,0,0,0,0), where x c,2 (0) is the x-coordinate of the second vehicle in the inertial coordinate system at the initial moment, y c,2 (0) is the position of the second vehicle in the inertial coordinate system at the initial moment, θ2(0) is the deflection angle of the second vehicle relative to the horizontal direction at the initial moment, v c,2 (0) is the linear velocity of the second vehicle in the direction of θ2(0) at the initial moment, w c,2 (0) is the angular velocity of the second vehicle at the initial moment, a v,2 (0) is the linear acceleration of the second vehicle at the initial moment, a w,2 (0) is the angular acceleration of the second vehicle at the initial moment; x c,3 (0) is the x-coordinate of the third vehicle in the inertial coordinate system at the initial moment, y c,3 (0) is the position of the third vehicle in the inertial coordinate system at the initial moment, θ3(0) is the deflection angle of the third vehicle relative to the horizontal direction at the initial moment, and v c,3 (0) is the linear velocity of the third vehicle in the direction θ3(0) at the initial moment, w c,3 (0) is the angular velocity of the third car at the initial moment, a v,3 (0) is the linear acceleration of the third vehicle at the initial moment, a w,3 (0) is the angular acceleration of the third vehicle at the initial moment. Considering that the maximum ranging value and maximum measuring direction angle value of the vehicle's onboard sensors are 3m and... The safe distance between vehicles is 1 meter. (Performance function is used.) The following vehicle is instructed to follow the lead vehicle at a desired relative distance of 2m and a desired relative direction angle of 0rad.

[0230] The design parameters for the observer-based controller are: α d =0.9, t d,s =1,t d,S =1,k S =100, k η =0.1, t f =5, η m =10, k1=0.01, k=40, k2=0.01, k3=0.1, p=3, simulate a vehicle platoon consisting of three vehicles.

[0231] Simulation results are as follows Figures 3 to 9 As shown, where Figure 3 The actual driving trajectory of a convoy of three vehicles is given. To further illustrate the cooperative performance of the vehicles under the action of the observer-based controller and the observation results of the observer, Figure 4 and Figure 5 The observation errors of the second and third vehicles are given separately. As shown in the figure, the observation error converges to 0 within the preset time. The distance cooperation error e of the second vehicle is also presented. cd,2 and angular cooperation error and its corresponding performance function Figure 6 and Figure 7 The distance cooperation error e of the third vehicle is given in the text. cd,2 and angular cooperation error and its corresponding performance function Figure 8 and Figure 9 As shown in the figure, it is easy to see that the cooperation error always moves within the preset performance function and converges to 0 within the preset time. That is, the multi-lane vehicle cooperation control is realized within the preset time, and while ensuring vehicle communication connectivity, it effectively avoids collisions between vehicles.

[0232] 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; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A preset-time vehicle cooperative control method with preset instantaneous steady-state performance, characterized in that, The method includes the following steps: Step 1: Construct from A convoy of vehicles is formed, and the first vehicle in the convoy is designated as the lead vehicle. For all vehicles in the convoy except the lead vehicle, a vehicle model containing model uncertainties is established. Step 2: Adopt a leader-following formation strategy to establish the queue relationship between vehicles under the constraints of relative distance and relative direction angle; Step 3: Design the first The vehicle's preset time observer; Specifically, this includes: the observed values ​​of the preset time observer. First derivative Represented as: （17） in, （18） （19） （20） （21） in It is an auxiliary variable; yes The derivative; , and All are intermediate variables; yes The derivative; These are design parameters, and they satisfy... ; and All of these are time parameters to be given, and , ; and These are design parameters, and , Satisfying inequalities ,in It is the first Uncertainties in vehicle modeling The first derivative, It is the first Uncertainties in vehicle modeling first derivative model The upper bound; It is the first The linear acceleration of the vehicle; It is the first The vehicle's accelerator or brake input control signal; It is the first The quality of the vehicle; It is the first The engine time constant of a vehicle; Step 4: Design the first The vehicle's control signals, and the first The preset time observers of the vehicles together constitute the first A preset time cooperative controller for vehicles based on preset time observers; Step 5: Take in sequence Then repeat steps 3-4 in sequence until the design of the preset time cooperative controller based on the preset time observer for all vehicles in the convoy except the lead vehicle is completed, thereby realizing preset time vehicle cooperative control that guarantees preset instantaneous steady-state performance.

2. The preset time vehicle cooperative control method with preset instantaneous steady-state performance according to claim 1, characterized in that, For the team's number A car, and The vehicle model containing the model uncertainty term is established as follows: （1） （2） （3） （4） （5） （6） （7） in It is the first The position of the vehicle's x-coordinate in the inertial coordinate system; yes The derivative; It is the first The position of the vehicle's ordinate in the inertial coordinate system; yes The derivative; It is the first The deflection angle of the vehicle relative to the horizontal direction; yes The derivative; It is the first The car is Linear velocity in the direction; yes The derivative; It is the first The angular velocity of the vehicle; yes The derivative; yes The derivative; It is the first The angular acceleration of the vehicle; yes The derivative; It is the first The vehicle's steering wheel inputs control signals; It is the first Uncertainties in vehicle modeling.

3. The preset time vehicle cooperative control method with preset instantaneous steady-state performance according to claim 2, characterized in that, Step 2 also includes: A leader-follower formation strategy is adopted, and a directed graph with a directed spanning tree is used to describe the communication relationships between vehicles; the aforementioned... The convoy of vehicles is broken down into A subsystem consisting of a lead vehicle and a follower vehicle; the lead vehicle in the convoy moves along a preset trajectory and is regarded as the root of the directed spanning tree of the directed graph.

4. The preset time vehicle cooperative control method with preset instantaneous steady-state performance according to claim 2, characterized in that, Step 2, the process of establishing the queue relationship between the vehicles, includes: Define any pair of leader-following vehicles, assuming the first vehicle in the convoy is... The car was the leader's car, the first in the convoy. The vehicle was a following vehicle. The relative distance between the lead car and the following car and relative direction angle for: （8） （9） in It is the first The position of the vehicle's x-coordinate in the inertial coordinate system; It is the first The position of the vehicle's ordinate in the inertial coordinate system; To ensure communication connectivity between vehicles, the relative distance constraints and relative direction angle constraints between vehicles are set as follows: （10） （11） in t Indicates time; It is the first The maximum ranging value of the vehicle's onboard sensors, and meets the following requirements. ; It is the first The maximum measurement orientation angle value of the vehicle's onboard sensors, and satisfying ; and The value depends on the measurement and sensing capabilities of the vehicle communication equipment; To prevent collisions between adjacent vehicles, the relative distance constraints between vehicles are further set as follows: （12） in The pre-set safe distance between vehicles, and meets the following requirements. ; Define vehicle cooperation errors, including: distance cooperation error and angle cooperation error; （13） （14） in It is distance cooperation error; It is an angular cooperation error; The desired relative distance is set, and it satisfies... ; The desired relative direction angle is set, and it satisfies... ; The performance function is used to constrain the collaborative error boundary: （15） （16） in , , , All are performance functions to be given, and satisfy... , .

5. A preset-time vehicle cooperative control method with preset instantaneous steady-state performance according to claim 4, characterized in that, The control signals in step 4 include: virtual control signals, accelerator or brake input control signals, and steering wheel input control signals.

6. A preset-time vehicle cooperative control method with preset instantaneous steady-state performance according to claim 5, characterized in that, In step 4, the first... The process of the vehicle's preset time cooperative controller based on a preset time observer includes: Design No. Virtual control signals for the vehicle: （28） （29） （30） （31） Design No. Vehicle accelerator or brake input control signals: （32） Design No. The vehicle's steering wheel inputs control signals: （33） in, （34） （35） （36） （37） （38） （39） （40） （41） （42） （43） （44） （45） （46） （47） （48） （49） （50） （51） （52） （53） （54） （55） （56） （57） （58） （59） （60） in , , , All are the first Virtual control signals for the vehicle; yes The derivative; yes The derivative; yes The derivative; yes The derivative; , , , , , , , , , , , , , , , , , , , , , , , , , , All are intermediate variables; It is the first The vehicle is based on the preset time parameters of the preset time cooperative controller of the preset time observer, and The preset time of the observer is greater than the preset time. ; , , , , , , , , , and All are positive design parameters to be given, and It is a positive integer that satisfies the inequality ; It is the first The deflection angle of the vehicle relative to the horizontal direction; It is the first The car is Linear velocity in the direction; yes The derivative; yes The derivative; yes The derivative; yes The derivative; yes The derivative; yes The derivative of .

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