A vehicle platoon state constrained finite-time control system and method

Abstract

The application discloses a kind of vehicle queue state constraint finite time control system and method, the vehicle queue controller used in the method includes state constraint module, virtual control input solving module, actual control input solving module and vehicle power control signal solving module.State constraint module is nonlinearly transformed with error system by finite time performance function;Virtual control input solving module obtains virtual control input based on error system;Actual control input solving module obtains actual control input according to virtual control input;Vehicle power control signal solving module obtains acceleration and deceleration signal according to actual control input.The application is aimed at slow distance adjustment, unstable queue and external interference in the process of vehicle following, and proposes a kind of vehicle queue distance adjustment method based on state constraint finite time control, so that vehicle queue reaches stability in finite time, significantly improves the response speed of vehicle following distance and the robust anti-interference performance of vehicle queue.

Description

Technical Field

[0001] This invention relates to a vehicle queuing state constraint finite-time control system and method, belonging to the field of automatic control systems. Background Technology

[0002] In recent years, with the continuous increase in car ownership, the resulting problems of resource consumption, environmental pollution, and traffic congestion have become increasingly prominent. Exploring more energy-efficient, environmentally friendly, and efficient modes of transportation has become a key research focus in the field of intelligent transportation. Vehicle platoon control is one of the important technologies of intelligent transportation systems and has received increasing attention. Vehicles in a platoon are interconnected during operation; the acceleration or deceleration of any vehicle can affect other vehicles and even lead to collisions and other traffic accidents. Therefore, effectively controlling each vehicle in the platoon to maintain a given distance is crucial to maintaining the stability of the entire platoon system.

[0003] In vehicle platoon control, the convergence speed of the distance error between adjacent vehicles is a crucial indicator for evaluating platoon performance. Most existing studies only yield convergence results based on Lyapunov asymptotic stability. Asymptotic stability converges exponentially the fastest, meaning that time-optimal control cannot be achieved under asymptotic stability, which impacts platoon performance. Furthermore, vehicles are susceptible to adverse factors such as uneven road surfaces and harsh driving environments, all of which affect platoon stability. Finite-time control techniques offer faster convergence speeds and stronger anti-interference capabilities than asymptotic stability. Currently, homogeneous finite-time control and terminal sliding mode finite-time control techniques have been further studied in vehicle platooning systems. The control law design process for homogeneous finite-time control is relatively simple, requiring only that the platoon system satisfy asymptotic stability and have negative homogeneity. However, this method cannot provide an upper bound expression for the finite convergence time. Although terminal sliding mode finite-time control technology can provide an upper bound expression for the specific convergence time, the convergence time largely depends on the initial value of the distance error between adjacent vehicles in the platoon. Furthermore, terminal sliding mode control produces a discontinuous control law, which can cause system chattering, easily leading to frequent acceleration and deceleration of vehicles during platooning operations, and even affecting the stability of vehicles within the platoon and the queue.

[0004] Therefore, in order to address the problems of the inability to quickly converge vehicle spacing during convoy operation and the inability to guarantee convoy stability under external interference, it is necessary to propose a high-quality vehicle convoy spacing controller with faster response speed and stronger robust performance from the perspective of time optimization, so as to achieve rapid adjustment of vehicle spacing. Summary of the Invention

[0005] The technical problem this invention aims to solve is to reduce the convergence time of the following distance error between adjacent vehicles during platooning, enabling the vehicle spacing to quickly approach a safe following distance while exhibiting good robustness. To address this technical problem, this invention proposes a finite-time control system and method for following distance in a vehicle platooning system based on a state-constrained performance function. The technical solution adopted by this invention is as follows:

[0006] A vehicle queuing state-constrained finite-time control system includes a state constraint module, a virtual control input solving module, an actual control input solving module, and a vehicle power control signal solving module connected in sequence.

[0007] The state constraint module is used to construct the finite-time performance function p. i (t), introducing a nonlinear function The error function e i (t) and finite-time performance function p i (t) undergoes a nonlinear transformation e i (t)=f(ε i )p i (t);

[0008] The virtual control input solution module is based on the error system of the state constraint function, and selects the error e. i The function (t) is used to construct a Lyapunov function and employ finite-time control techniques to obtain the virtual control input β that enables the vehicle state variables to converge rapidly in finite time. i (t);

[0009] The actual control input solving module is used to reconstruct the Lyapunov function based on the error system obtained from the nonlinear transformation in the state constraint module and the virtual control input obtained from the virtual control input solving module. Then, it further obtains the actual control input u using finite-time control techniques. i (t);

[0010] The vehicle power control signal solving module is used to obtain vehicle acceleration and deceleration control signals based on the actual control input obtained by the actual control input solving module. When the actual control input is greater than 0, the vehicle accelerates; when the actual control input is less than 0, the vehicle decelerates. Furthermore, the acceleration and deceleration execution command signals to achieve a safe following distance are obtained based on the acceleration and deceleration control signals.

[0011] Furthermore, the actual control input u i (t) is:

[0012]

[0013] In the formula, k1 represents the adjustment coefficient for the distance error caused by the driver's reaction time, k2 represents the proportionality coefficient of braking distance to the square of speed, and v i Let be the speed of the i-th vehicle. m is a constant i Let τ be the mass of the i-th vehicle. i Let β be the engine time constant. i (t) represents the virtual control law, ξ i This is the new error after error transformation. Where g i (v i ,v i-1 ,a i ) and f i (v i ,a i Both φ and φ are nonlinear functions of velocity and acceleration. i (t) is a function of time t, ε i It is the error e i (t) Error correlation quantity after nonlinear transformation, z2>0, γ>0 are actual control law parameters.

[0014] The vehicle queue state constraint finite-time control method proposed in this invention mainly includes the following steps:

[0015] (1) Establish a dynamic model of the vehicle platoon system, mainly including a mathematical model of the secondary vehicle spacing error and a single vehicle dynamic model;

[0016] (2) Establish error state variables, transform the vehicle platoon system dynamics model into a third-order nonlinear error model, and determine the error state variable x of the i-th vehicle in the vehicle platoon system. i Control input u i and output quantity y i ;

[0017] (3) Establish the finite-time performance function

[0018]

[0019] Where k and λ are optional positive parameters, T is the fixed convergence time, and p T To maximize the allowable steady-state tracking error, the established finite-time performance function satisfies: 1) p i (t)>0;2) 3) The set fixed convergence time W() is the Lambert W function;

[0020] (4) The secondary vehicle spacing error between the i-th vehicle and the (i-1)-th vehicle in the system is calculated as ei (t)=f(ε i )p i (t) undergoes a nonlinear mapping transformation, the nonlinear function f(ε) i ) is about ε i A function of ε(t), i (t) is the error e i (t) Error correlation quantity after nonlinear transformation;

[0021] (5) Construct a virtual control law β for the finite-time performance function in the virtual control input solution module of the vehicle queue state constraint finite-time controller. i (t);

[0022] (6) The actual control input solution module of the vehicle queue state constraint finite-time controller obtains the actual control input u based on the system's third-order error model and the virtual control input. i (t);

[0023] (7) The vehicle power control signal solving module solves the signal based on the actual control input u. i (t) Acquire vehicle acceleration and deceleration control signals, and further obtain acceleration and deceleration execution command signals based on the acquired acceleration and deceleration control signals to achieve fast and accurate tracking of target vehicle distance between vehicle queues within a limited time.

[0024] Preferably, in step (5), the construction steps of the virtual control law based on the finite-time performance function are as follows:

[0025] (8) Based on the nonlinear mapping transformation e performed in step (4) i (t)=f(ε i )p i (t), where Taking the first derivative of the mapping transformation, we obtain ε. i (t) and e i The relationship between (t);

[0026] (9) Introducing virtual control input β i (t), and then perform another error coordinate transformation, let ξ i (t)=e i (t)-β i (t), ξ i This represents the new error after coordinate transformation.

[0027] (10) Select the Lyapunov function and determine the virtual control law β that stabilizes the vehicle platoon closed-loop control system. i (t) and control law parameters.

[0028] Preferably, in step (2), the state variables of the vehicle platoon system dynamics model include the distance between adjacent vehicles in the platoon, the speed of a single vehicle in the platoon, and the acceleration of a single vehicle, and the control input is the desired target acceleration of a single vehicle. The state variables of the error model after nonlinear transformation include the distance error between adjacent vehicles in the platoon, the first derivative of the distance error, and the second derivative of the distance error, and the control input is still the desired target acceleration of a single vehicle.

[0029] Compared to Lyapunov's asymptotically stable system, which converges exponentially, the present invention offers the advantage of enabling the vehicle platooning control system's state variables to rapidly converge to the equilibrium point within a set fixed time by constructing a state-constrained performance function. This fixed time does not depend on the initial spacing error of the vehicle platooning system. Therefore, unlike homogeneous finite-time control, which cannot provide a specific upper bound on the convergence time, and terminal sliding mode finite-time control, whose convergence time depends on the initial error of the vehicle platooning, the proposed finite-time control method exhibits a faster response speed. Furthermore, the system's external disturbance suppression capability can be adjusted by modifying the finite-time control law parameters. The present invention's technical solution can also effectively suppress the impact of disturbances on the vehicle following distance adjustment process, improving the robustness of the vehicle platooning system. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the vehicle queuing following distance control system.

[0031] Figure 2 This is a schematic diagram illustrating the finite-time control principle of the vehicle queuing system for following vehicles. Detailed Implementation

[0032] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0033] Figure 1 A schematic diagram of a vehicle platooning following distance control system is provided. It includes several vehicles traveling in the same lane, each equipped with an onboard sensor. Vehicles in the platoon can obtain the status information (displacement x) of the vehicle ahead through these sensors. i-1 Speed ​​v i-1 and acceleration a i-1 (etc.) When the distance between adjacent vehicles is greater than the safe driving distance, the following vehicle accelerates to reduce the distance between the two vehicles, thus improving lane utilization; conversely, when the distance between adjacent vehicles is less than the safe driving distance, the following vehicle decelerates to increase the distance between the two vehicles, thus improving driving safety.

[0034] Figure 2A schematic diagram illustrating the finite-time control principle of a vehicle platooning system for following distance is provided. This includes modules for secondary vehicle spacing error calculation, state constraints, virtual control input solving, actual control input solving, vehicle power control signal solving, and vehicle power system adjustment. The vehicle acquires the status information x of the vehicle ahead via onboard sensors. i-1 v i-1 and a i-1 The secondary vehicle spacing error calculation module calculates the secondary vehicle spacing error signal based on the vehicle's and the preceding vehicle's state information combined with the vehicle spacing strategy. In the state constraint module, a finite-time performance function is first constructed, and then a new error model is obtained by nonlinearly transforming the performance function and the secondary vehicle spacing error function. The virtual control input solution module obtains the virtual control input that enables the vehicle's state variables to converge quickly in finite time based on the error system of the state constraint function. The actual control input solution module obtains the actual control input based on the third-order error system and the virtual control input. The vehicle power control signal solution module obtains the vehicle acceleration / deceleration control signal based on the actual control input, and further obtains the acceleration / deceleration execution command signal to achieve a safe following distance based on the acceleration / deceleration control signal. The vehicle power system adjustment module performs acceleration / deceleration operations based on the obtained acceleration / deceleration execution command signal, making real-time adjustments to the vehicle.

[0035] The finite-time control method for vehicle queue state constraints adopted is as follows:

[0036] (1) Establish a dynamic model of the vehicle platoon system, mainly including a mathematical model of the secondary vehicle spacing error and a single-vehicle dynamic model. The mathematical model of the secondary vehicle spacing error is expressed as:

[0037] d i =x i-1 -x i -L i -S (1)

[0038] In the formula, d i x represents the distance error between adjacent vehicles. i (i = 1, 2, ..., n) represents the position of the i-th vehicle, L i Let S be the length of the i-th vehicle and S be the safe parking distance, satisfying... k1 represents the adjustment coefficient for the distance error caused by the driver's reaction time, k2 represents the proportionality coefficient of braking distance to the square of speed, and v i (i = 1, 2, ..., n) represents the speed of the i-th vehicle.

[0039] The single-vehicle dynamics model is represented as follows:

[0040]

[0041] In the formula, ai (i = 1, 2, ..., n) represents the acceleration of the i-th vehicle, m i Let F be the mass of the i-th vehicle. e,i This indicates the driving force generated by the engine, satisfying τ i U is the engine time constant. i For controlling input. The air resistance is represented by ρ, where ρ is the air density, A is the cross-sectional area of ​​the vehicle, C is the drag coefficient, and F is the air resistance coefficient. f,i =m i gfcosθ represents rolling resistance, where g is the acceleration due to gravity, f is the rolling resistance coefficient, θ is the road gradient, and F g,i =m i gsinθ is the drag force caused by gravity, D i It is an unknown external disturbance caused by factors such as strong winds and uneven road surfaces, and it is assumed that the disturbance is bounded.

[0042] Combining the second-order vehicle spacing error, the dynamic model of the vehicle platoon system can be obtained from the single-vehicle dynamics model as follows:

[0043]

[0044] In the formula, g is a constant. i (v i ,v i-1 ,a i ) and f i (v i ,a i Both are nonlinear functions of velocity and acceleration, and satisfy the following conditions:

[0045] g i (v i ,v i-1 ,a i ) = v i-1 -2k2v i a i -k1a i (4)

[0046]

[0047] (2) Select the state error variable as e i , let e i =d i The dynamic model of the vehicle platoon system can be further transformed into the following third-order nonlinear form:

[0048]

[0049] In the formula,

[0050] (3) Establish the finite-time performance function

[0051]

[0052] Where k and λ are optional positive parameters, T is the fixed convergence time, and p T To maximize the allowable steady-state tracking error, the established finite-time performance function satisfies: 1) p i (t)>0;2) 3) The set fixed convergence time W() is the Lambert W function;

[0053] (4) The secondary vehicle spacing error between the i-th vehicle and the (i-1)-th vehicle in the system is calculated as e i (t)=f(ε i )p i (t) undergoes a nonlinear mapping transformation, the nonlinear function f(ε) i ) is about ε i A function of ε(t), i (t) is the error e i (t) Error correlation quantity after nonlinear transformation;

[0054] (5) Construct a virtual control law β for the finite-time performance function in the virtual control input solution module of the vehicle queue state constraint finite-time controller. i (t), mainly includes the following steps:

[0055] 1) Based on the nonlinear mapping transformation e obtained in step (4) i (t)=f(ε i )p i (t), where Satisfy -1 <f(ε i Since -p < 1, therefore -p i (t) <e i (t) <p i (t), further differentiating the nonlinear transformation yields

[0056]

[0057] For ease of writing, we construct two functions φ with respect to time t. i (t) and Its expression is as follows:

[0058]

[0059] The system error model after nonlinear mapping transformation is then converted into

[0060]

[0061] 2) Let the error transformation ξ i (t)=e i (t)-β i (t), select the first Lyapunov function Taking the derivative of V1(t), we get

[0062]

[0063] The first derivative of the virtual control law is chosen as

[0064]

[0065] In the formula, z1 is a virtual control law parameter and satisfies a value greater than 0. Further...

[0066]

[0067] 3) Integrate the first derivative of the virtual control law to obtain the virtual control law β. i (t).

[0068] (6) In the actual control input solution module of the vehicle queue state constraint finite time controller, the virtual control input β determined by combining equations (10) and (12) is... i (t) and the first derivative of the virtual control law Choose the second Lyapunov function as Differentiating V2(t) yields

[0069]

[0070] Selecting the actual control law

[0071]

[0072] In the formula, z2>0 and γ>0 are the parameters of the actual control law. Furthermore,

[0073]

[0074] When D i When = 0, then Where z = min{z1, z2};

[0075] When D i When ≠0, then Integrating both sides of the inequality over time t∈(0,T], i.e.

[0076]

[0077] Furthermore, as can be seen from step (4), ||e i (t)|| 2 ≤||ε i || 2 (k+p T ) 2 ,so

[0078]

[0079] Therefore, when external disturbances are present, the L2 gain of the system from the disturbance input to the closed-loop system output is no greater than [value missing]. That is, the system can guarantee strong robustness under the actual input control law with finite time under the state constraint.

[0080] (7) The vehicle power control signal solving module solves the signal based on the actual control input u. i (t) Acquire vehicle acceleration and deceleration control signals, and further obtain acceleration and deceleration execution command signals based on the acquired acceleration and deceleration control signals to achieve fast and accurate tracking of target vehicle distance between vehicle queues within a limited time.

Claims

1. A vehicle queue state-constrained finite-time control system, characterized in that, It includes a state constraint module, a virtual control input solution module, an actual control input solution module, and a vehicle power control signal solution module connected in sequence; The state constraint module is used to construct the finite-time performance function p. i (t), introducing a nonlinear function The error function e i (t) and finite-time performance function p i (t) undergoes a nonlinear transformation e i (t)=f(ε i )p i (t); nonlinear function f(ε) i ) is about ε i A function of ε(t), i (t) is the error e i (t) Error correlation quantity after nonlinear transformation; The virtual control input solution module is based on the error system of the state constraint function, and selects the error e. i The function (t) is used to construct a Lyapunov function and employ finite-time control techniques to obtain the virtual control input β that enables the vehicle state variables to converge rapidly in finite time. i (t); The actual control input solving module is used to reconstruct the Lyapunov function based on the error system obtained from the nonlinear transformation in the state constraint module and the virtual control input obtained from the virtual control input solving module. Then, it further obtains the actual control input u using finite-time control techniques. i (t); The vehicle power control signal solving module is used to obtain vehicle acceleration and deceleration control signals based on the actual control input obtained by the actual control input solving module. When the actual control input is greater than 0, the vehicle accelerates. When the actual control input is less than 0, the vehicle decelerates, and further acceleration and deceleration execution command signals to achieve a safe following distance are obtained based on the acceleration and deceleration control signals.

2. The vehicle queue state constraint finite-time control system according to claim 1, characterized in that, Actual control input u i (t) is: In the formula, k1 represents the adjustment coefficient for the distance error caused by the driver's reaction time, k2 represents the proportionality coefficient of braking distance to the square of speed, and v i Let be the speed of the i-th vehicle. m is a constant i Let τ be the mass of the i-th vehicle. i Let β be the engine time constant. i (t) represents the virtual control law, ξ i This is the new error after error transformation. Where g i (v i ,v i-1 ,a i ) and f i (v i ,a i Both φ and φ are nonlinear functions of velocity and acceleration. i (t) is a function of time t, ε i It is the error e i (t) Error correlation quantity after nonlinear transformation, z2>0, γ>0 are actual control law parameters.

3. A finite-time control method for vehicle queue state constraints, characterized in that, Includes the following steps: (1) Establish a dynamic model of the vehicle platoon system, mainly including a mathematical model of the secondary vehicle spacing error and a single vehicle dynamic model; (2) Establish error state variables, transform the vehicle platoon system dynamics model into a third-order nonlinear error model, and determine the error state variable x of the i-th vehicle in the vehicle platoon system. i Control input u i and output quantity y i ; (3) Establish the finite-time performance function p i (t); (4) The secondary vehicle spacing error between the i-th vehicle and the (i-1)-th vehicle in the system is calculated as e i (t)=f(ε i )p i (t) undergoes a nonlinear mapping transformation, the nonlinear function f(ε) i ) is about ε i A function of ε(t), i (t) is the error e i (t) Error correlation quantity after nonlinear transformation; (5) Construct a virtual control law β for the finite-time performance function in the virtual control input solution module of the vehicle queue state constraint finite-time controller. i (t); (6) The actual control input solution module of the vehicle queue state constraint finite-time controller obtains the actual control input u based on the system's third-order error model and the virtual control input. i (t); (7) The vehicle power control signal solving module solves the signal based on the actual control input u. i (t) Acquire vehicle acceleration and deceleration control signals, and further solve for acceleration and deceleration execution command signals based on the acquired acceleration and deceleration control signals to achieve fast and accurate tracking of target vehicle distance between vehicle queues within a limited time.

4. The vehicle queue state constraint finite-time control method according to claim 3, characterized in that, The finite-time performance function is: Where k and λ are optional positive parameters, T is the fixed convergence time, and p T To maximize the allowable tracking steady-state error, the established finite-time performance function satisfies: 1) p i (t)>0;2) 3) The set fixed convergence time W() is the Lambert W function.

5. The vehicle queue state constraint finite-time control method according to claim 3, characterized in that, In step (5), the construction steps of the virtual control law based on the finite-time performance function are as follows: Based on the nonlinear mapping transformation e performed in step (4) i (t)=f(ε i )p i (t), where Taking the first derivative of the mapping transformation, we obtain ε. i (t) and e i The relationship between (t); Introducing virtual control input β i (t), and then perform another error coordinate transformation, let ξ i (t)=e i (t)-β i (t), ξ i This represents the new error after coordinate transformation; Selecting a Lyapunov function, determine the virtual control law β that stabilizes the vehicle platoon closed-loop control system. i (t) and control law parameters.

6. The vehicle queue state constraint finite-time control method according to claim 3, characterized in that, In step (2), the state variables of the vehicle queuing system dynamics model include the distance between adjacent vehicles in the vehicle queuing, the speed of a single vehicle in the vehicle queuing, and the acceleration of a single vehicle. The control input is the desired target acceleration of a single vehicle. The error model state variables after nonlinear transformation include the distance error between adjacent vehicles in the vehicle queuing, the first derivative of the distance error, and the second derivative of the distance error. The control input is still the desired target acceleration of a single vehicle.

7. The vehicle queue state constraint finite-time control method according to claim 3, characterized in that, A dynamic model of the vehicle platooning system is established, mainly including a mathematical model of the secondary vehicle spacing error and a single-vehicle dynamic model. The mathematical model of the secondary vehicle spacing error is expressed as follows: d i =x i-1 -x i -L i -S (1) In the formula, d i x represents the distance error between adjacent vehicles. i Let L be the position of the i-th car. i Let S be the length of the i-th vehicle and S be the safe parking distance, satisfying... k1 represents the adjustment coefficient for the distance error caused by the driver's reaction time, k2 represents the proportionality coefficient of braking distance to the square of speed, and v i Let be the speed of the i-th vehicle, where i = 1, 2, ..., n; The single-vehicle dynamics model is represented as follows: In the formula, a i Let m be the acceleration of the i-th vehicle. i Let F be the mass of the i-th vehicle. e,i This indicates the driving force generated by the engine, satisfying τ i U is the engine time constant. i To control the input, The air resistance is represented by ρ, where ρ is the air density, A is the cross-sectional area of ​​the vehicle, C is the drag coefficient, and F is the air resistance coefficient. f,i =m i gfcosθ represents rolling resistance, where g is the acceleration due to gravity, f is the rolling resistance coefficient, θ is the road gradient, and F g,i =m i gsinθ is the drag force caused by gravity, D i It is an unknown external disturbance caused by factors such as strong winds and uneven road surfaces, and it is assumed that the disturbance is bounded.

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