CN114995454A - Vehicle queue state constraint finite time control system and method - Google Patents

Abstract

The invention discloses a vehicle platoon state constraint limited time control system and method. The vehicle platoon controller adopted in the method comprises a state constraint module, a virtual control input solving module, an actual control input solving module and a vehicle dynamic control signal solving module. The state constraint module performs nonlinear transformation with the error system through the performance constraint function; the virtual control input solving module obtains the virtual control input based on the error system; the actual control input solving module obtains the actual control input according to the virtual control input; the vehicle dynamic control signal solving module obtains the actual control input according to the actual The control input is used to acquire acceleration and deceleration signals. Aiming at slow spacing adjustment, unstable queues and external disturbances in the process of team following, the invention proposes a team spacing adjustment method based on state constraints and limited time control, so that the team can achieve stability in a limited time and significantly improve the team following. The response speed of the spacing and the robust anti-jamming performance of the fleet.

Description

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

technical field

The invention relates to a vehicle queue state constraint limited time control system and method, and belongs to the field of automatic control systems.

Background technique

In recent years, with the continuous increase of car ownership, the resulting problems such as resource consumption, environmental pollution, and traffic congestion have become increasingly prominent. Vehicle queuing control is one of the important technologies of intelligent transportation system, which has received more and more attention. The vehicles in the fleet are coupled with each other during the driving process, and the acceleration and deceleration of any vehicle will affect other vehicles and even cause traffic accidents such as collisions. Therefore, it is critical to effectively control each vehicle in the fleet to maintain a given distance between vehicles, thereby maintaining the stability of the entire fleet system.

In the vehicle platoon control, the convergence speed of the distance error between adjacent vehicles is an important index to evaluate the driving performance of the platoon. In most of the existing studies, only the convergence results based on Lyapunov asymptotic stability can be obtained. The asymptotic stability converges the fastest in the exponential form, which means that the time-optimal control effect cannot be achieved under the asymptotic stability, which will affect the fleet. driving performance. In addition, vehicles are easily affected by unfavorable factors such as uneven road surface and harsh driving environment during the driving of the fleet, which will affect the stability of the fleet. The finite-time control technique has faster convergence speed and stronger anti-interference performance than asymptotic stabilization. At present, the homogeneous finite time control technology and the terminal sliding mode finite time control technology have been further studied in the vehicle platoon system. Among them, the control law design process based on homogeneous finite-time control technology is relatively simple, as long as the fleet system is asymptotically stable and has negative homogeneity, but this method cannot give the upper bound expression of finite convergence time. Although the finite-time control technology based on terminal sliding mode can give the upper bound expression of the specific convergence time, the convergence time largely depends on the initial value of the distance error between adjacent vehicles of the fleet, and the terminal sliding mode control obtains a This is a discontinuous control law, which will cause the system to generate buffeting, which may easily cause frequent acceleration and deceleration of vehicles during the driving process of the fleet, and even affect the stability of the fleet and the fleet.

Therefore, it is necessary to propose a high-quality vehicle platoon with faster response speed and stronger robust performance from the perspective of time optimization in order to solve the problems that the distance cannot be quickly converged and the stability of the platoon cannot be guaranteed under external interference during the driving process of the platoon. Gap controller for quick adjustment of vehicle spacing.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to reduce the convergence time of the distance error between adjacent vehicles when the vehicles are platooning, so that the distance between the vehicles quickly tends to the safe following distance, and has good robust performance. Aiming at the technical problem, the present invention proposes a limited time control system and method for the following distance of a vehicle platoon system based on a state constraint performance function. The technical scheme adopted in the present invention is:

A vehicle platoon state-constrained finite-time control system includes a state constraint module, a virtual control input solution module, an actual control input solution module, and a vehicle dynamic control signal solution module connected in sequence;

将误差函数e_i(t)与性能约束函数p_i(t)进行非线性变换e_i(t)＝f(ε_i)p_i(t)；The state constraint module is used to construct a performance constraint function p _i (t), introducing a nonlinear function

Perform a nonlinear transformation on the error function e _i (t) and the performance constraint function p _i (t) e _i (t)=f(ε _i )p _i (t);

The virtual control input solving module is based on the error system of the state constraint function, selects the function about the error e _i (t), and by constructing the Lyapunov function, with the help of the finite time control technology, is used to obtain a virtual vehicle state variable that quickly converges in a finite time. control input β _i (t);

The actual control input solving module is used to construct the Lyapunov function again according to the error system obtained by the nonlinear transformation in the state constraint module, combined with the virtual control input obtained in the virtual control input solving module, and further obtain the actual control according to the finite time control technology. input u _i (t);

The vehicle power control signal solving module is used to obtain the vehicle acceleration and deceleration control signal according to 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 is accelerated. Decelerate, and further obtain the acceleration and deceleration execution command signal for realizing the safe following distance according to the acceleration and deceleration control signal.

Further, the actual control input _ui (t) is:

为常数，m_i为第i辆车的质量，τ_i为发动机时间常数，β_i(t)为虚拟控制律，ξ_i为误差变换后的新误差，

其中g_i(v_i,v_i-1,a_i)和f_i(v_i,a_i)均为关于速度和加速度的非线性函数，φ_i(t)为关于时间t的函数，ε_i是误差e_i(t)非线性变换后的误差相关量，z₂>0,γ＞0为实际控制律参数。In the formula, k ₁ represents the spacing error adjustment coefficient caused by the driver's reaction time, k ₂ represents the proportional coefficient of the braking distance and the square of the speed, v _i is the speed of the ith vehicle,

is a constant, m _i is the mass of the i-th vehicle, τ _i is the engine time constant, β _i (t) is the virtual control law, ξ _i is the new error after error transformation,

where g _i (v _i ,v _i-1 ,a _i ) and f _i (v _i ,a _i ) are nonlinear functions of velocity and acceleration, φ _i (t) is a function of time t, ε _i is the error correlation quantity after nonlinear transformation of error e _i (t), z ₂ >0, γ>0 are the actual control law parameters.

The vehicle platoon state constraint limited time control method proposed by the technical solution of the present invention mainly includes the following steps:

(1) Establish a vehicle platooning system dynamics model, which mainly includes a mathematical model of the secondary vehicle spacing error and a single vehicle dynamics model;

(2) Establish the error state variable, convert the dynamic model of the vehicle platoon system to a third-order nonlinear error model, and determine the error state quantity _xi , control input _ui and output quantity yi of the _i -th vehicle in the vehicle platoon system ;

(3) Establish a finite-time performance function

3)

所设定的固定收敛时间

W()为Lambert W函数；Where k and λ are optional positive parameters, T is the set fixed convergence time, and p _T is the maximum allowable tracking steady-state error. The established finite-time performance function satisfies: 1) p _i (t)>0; 2)

3)

Set fixed convergence time

W() is the Lambert W function;

(4) Perform nonlinear mapping transformation on the secondary inter-vehicle distance error between the i-th vehicle and the i-1-th vehicle in the system according to e _i (t)=f(ε _i )p _i (t), the nonlinear function f( ε _i ) is a function of ε _i (t), and ε _i (t) is the error correlation quantity after nonlinear transformation of error e _i (t);

(5) Build a virtual control law β _i (t) about the finite-time performance function in the virtual control input solving module of the vehicle platoon state-constrained finite-time controller;

(6) The actual control input solving module of the vehicle platoon state-constrained finite-time controller obtains the actual control input u _i (t) according to the third-order error model of the system and the virtual control input;

(7) The vehicle power control signal solving module obtains the vehicle acceleration and deceleration control signal according to the actual control input u _i (t), and further obtains the acceleration and deceleration execution instruction signal according to the obtained acceleration and deceleration control signal according to the acceleration and deceleration signals, so as to realize the vehicle queue Fast and accurate tracking with limited time between target vehicles.

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

将映射变换进行一阶求导，得到ε_i(t)跟e_i(t)的关系；(8) Based on the nonlinear mapping transformation e _i (t)=f(ε _i )p _i (t) performed in step (4), where

The first-order derivative of the mapping transformation is performed to obtain the relationship between ε _i (t) and e _i (t);

(9) Introduce virtual control input β _i (t), and perform error coordinate transformation again, let ξ _i (t)=e _i (t)-β _i (t), ξ _i is the new error after coordinate transformation.

(10) Select the Lyapunov function to determine the virtual control law β _i (t) and control law parameters to stabilize the vehicle platoon closed-loop control system.

Preferably, in step (2), the state variables of the vehicle queue system dynamics model include the distance between adjacent vehicles in the vehicle queue, the speed and acceleration of a single vehicle in the vehicle queue, and the control input is the expected target acceleration of a single vehicle. The state quantity of the error model after nonlinear transformation includes the adjacent vehicle spacing error of the vehicle queue, the first-order derivative function of the vehicle spacing error, and the second-order derivative function of the vehicle spacing error. The control input is still the desired target acceleration of a single vehicle.

Compared with the Lyapunov asymptotic stability, the system can only converge at an exponential speed. The beneficial effect of the present invention is that the state variables of the vehicle platoon control system can quickly converge to the equilibrium point within a set fixed time by constructing a state constraint performance function. The fixed fixed time does not depend on the initial distance error of the vehicle platoon system, so it is different from the homogeneous finite time control, which cannot give the upper bound of the specific convergence time and the terminal sliding mode finite time control. The convergence time depends on the initial error of the vehicle platoon, so the The proposed finite-time control method can have a faster response speed than the previous two. At the same time, the adjustment of the external disturbance suppression capability of the system can be realized by adjusting the parameters of the limited time control law, and the technical solution of the present invention can also effectively suppress the influence of disturbance on the adjustment process of the vehicle following distance and improve the robustness of the vehicle platoon system. .

Description of drawings

Figure 1 is a schematic diagram of the structure of a vehicle queue following distance control system.

Figure 2 is a schematic diagram of the limited time control principle of the vehicle queuing system following the vehicle spacing.

Detailed ways

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

Figure 1 shows a schematic diagram of the structure of the vehicle platoon following distance control system. Including several vehicles running in the same lane, each vehicle is equipped with on-board sensors, the vehicles in the fleet can obtain the status information of the vehicle ahead (displacement x _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 rear vehicle accelerates to reduce the distance between the two vehicles and improves the lane utilization rate; on the contrary, when the distance between adjacent vehicles is smaller than the safe driving distance, the rear vehicle decelerates to increase the distance between the two vehicles, improving the driving safety.

Figure 2 shows the schematic diagram of the limited time control principle of the vehicle queuing system following the vehicle spacing. It includes a secondary vehicle distance error calculation module, a state constraint module, a virtual control input solution module, an actual control input solution module, a vehicle power control signal solution module, and a vehicle power system adjustment module. The vehicle obtains the state information x _i-1 , v _i-1 and a _i-1 of the vehicle ahead through the on-board sensor, and the secondary vehicle spacing error calculation module solves the secondary vehicle spacing error according to the state information of the vehicle and the preceding vehicle combined with the vehicle spacing strategy Signal. In the state constraint module, a performance constraint function is first constructed, and then a new error model is obtained by nonlinearly transforming the performance function and the quadratic distance error function. The virtual control input solving module obtains the virtual control input that makes the vehicle state variables converge quickly in a limited time based on the error system of the state constraint function. The actual control input solving module obtains the actual control input according to the third-order error system and the virtual control input. The vehicle power control signal solving module obtains the vehicle acceleration and deceleration control signal according to the actual control input, and further obtains the acceleration and deceleration execution instruction signal for realizing the safe following distance according to the acceleration and deceleration control signal. The vehicle power system adjustment module performs acceleration and deceleration operations according to the obtained acceleration and deceleration execution command signals, and performs real-time adjustment of the own vehicle.

The vehicle platoon state-constrained finite-time control method adopted is as follows:

(1) Establish the vehicle platoon system dynamics model, which mainly includes the vehicle secondary vehicle spacing error mathematical model and the single vehicle dynamics model. The mathematical model of the secondary vehicle spacing error of the vehicle is expressed as:

d _i =x _i-1 -x _i -L _i -S (1)

k₁表示驾驶员反应时间所引起的间距误差调整系数，k₂表示刹车距离跟速度平方的比例系数，v_i(i＝1,2,…,n)为第i辆车的速度。In the formula, d _i is the distance error between adjacent vehicles, _xi (i=1,2,...,n) is the position of the i-th vehicle, Li is the body length of the _i -th vehicle, S is the safe parking distance, Satisfy

k ₁ represents the spacing error adjustment coefficient caused by the driver's reaction time, k ₂ represents the proportional coefficient between the braking distance and the square of the speed, and v _i (i=1,2,...,n) is the speed of the i-th vehicle.

The bicycle dynamics model is expressed as:

τ_i为发动机时间常数，u_i为控制输入。

表示空气阻力,ρ为空气密度，A为车辆的横截面面积，C为空气阻力系数，F_f,i＝m_igfcosθ表示滚动阻力，g为重力加速度，f为滚动阻力系数，θ为道路坡度，F_g,i＝m_igsinθ是重力引起的阻力，D_i是由强风、路面不平等因素引起的未知外界扰动，并假设扰动有界。In the formula, a _i (i=1,2,...,n) is the acceleration of the i-th vehicle, m _i is the mass of the i-th vehicle, and _Fe,i represents the driving force generated by the engine, which satisfies

τ _i is the engine time constant and _ui is the control input.

represents the air resistance, ρ is the air density, A is the cross-sectional area of the vehicle, C is the air resistance coefficient, F _f,i = m _i gfcosθ is the rolling resistance, g is the acceleration of gravity, f is the rolling resistance coefficient, and θ is the road gradient , F _g,i = m _i gsinθ is the resistance caused by gravity, D _i is the unknown external disturbance caused by strong wind and uneven road surface, and the disturbance is assumed to be bounded.

Combined with the secondary vehicle spacing error, the vehicle platoon system dynamics model can be obtained from the single vehicle dynamics model, which is expressed as:

为常数，g_i(v_i,v_i-1,a_i)和f_i(v_i,a_i)均为关于速度和加速度的非线性函数，且满足In the formula,

is a constant, g _i (v _i ,v _i-1 ,a _i ) and f _i (v _i ,a _i ) are nonlinear functions of velocity and acceleration, and satisfy

g _i (v _i ,v _i-1 ,a _i )=v _i-1 -2k ₂ v _i a _i -k ₁ a _i (4)

(2) The state error variable is selected as e _i , and e _i =d _i , the vehicle platoon system dynamics model can be further transformed into the following third-order nonlinear form:

In the formula,

(3) Establish a finite-time performance function

3)

所设定的固定收敛时间

W()为Lambert W函数；Where k and λ are optional positive parameters, T is the set fixed convergence time, and p _T is the maximum allowable tracking steady-state error. The established finite-time performance function satisfies: 1) p _i (t)>0; 2)

3)

Set fixed convergence time

W() is the Lambert W function;

(4) Perform nonlinear mapping transformation on the secondary inter-vehicle distance error between the i-th vehicle and the i-1-th vehicle in the system according to e _i (t)=f(ε _i )p _i (t), the nonlinear function f( ε _i ) is a function of ε _i (t), and ε _i (t) is the error correlation quantity after nonlinear transformation of error e _i (t);

(5) The virtual control law β _i (t) about the finite-time performance function is constructed in the virtual control input solving module of the vehicle platoon state-constrained finite-time controller, which mainly includes the following steps:

满足-1<f(ε_i)<1，因此-p_i(t)<e_i(t)<p_i(t)，进一步对非线性变换求导得到1) Based on the nonlinear mapping transformation e _i (t)=f(ε _i )p _i (t) obtained in step (4), where

Satisfy -1<f(ε _i )<1, so -p _i (t)<e _i (t)<p _i (t), and further derive the nonlinear transformation to get

其表达式如下：For the convenience of writing, two functions φ _i (t) and

Its expression is as follows:

Then, after the nonlinear mapping transformation, the systematic error model is transformed into

对V₁(t)求导，得到2) Let the error transformation ξ _i (t)=e _i (t)-β _i (t), select the first Lyapunov function

Derivative with respect to V ₁ (t), we get

The first derivative of the virtual control law is chosen as

In the formula, z ₁ is the virtual control law parameter and satisfies that it is greater than 0, and further

3) Integrate the first-order derivative function of the virtual control law to obtain the virtual control law β _i (t).

选择第二个Lyapunov函数为

对V₂(t)求导得到(6) In the actual control input solving module of the vehicle platoon state-constrained finite-time controller, the virtual control input β _i (t) and the first-order derivative function of the virtual control law determined by the combination of equations (10) and (12) are used.

Choose the second Lyapunov function as

Derivation with respect to V ₂ (t) gives

Choose the actual control law

In the formula, z ₂ >0, γ>0 are the actual control law parameters. further,

其中z＝min{z₁,z₂}；When D _i = 0, then

where z=min{z ₁ ,z ₂ };

对不等式两边在时间t∈(0,T]进行积分，即When D _i ≠ 0, then

Integrate both sides of the inequality at time t∈(0,T], i.e.

所以Further, it can be known from step (4) that,

so

即系统在该状态约束有限时间实际输入控制律作用下能够保证强鲁棒性。Therefore, when there is external disturbance, the system L2 gain from disturbance input to closed _- loop system output is not greater than

That is to say, the system can guarantee strong robustness under the action of the state-constrained finite-time actual input control law.

(7) The vehicle power control signal solving module obtains the vehicle acceleration and deceleration control signal according to the actual control input u _i (t), and further obtains the acceleration and deceleration execution instruction signal according to the obtained acceleration and deceleration control signal according to the acceleration and deceleration signals, so as to realize the vehicle queue Fast and accurate tracking with limited time between target vehicles.

Claims (7)

1. A vehicle platoon state constraint finite time control system, characterized in that it comprises 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 a performance constraint function p _i (t), introducing a nonlinear function

Perform a nonlinear transformation on the error function e _i (t) and the performance constraint function p _i (t) e _i (t)=f(ε _i )p _i (t); The virtual control input solving module is based on the error system of the state constraint function, selects the function about the error e _i (t), and by constructing the Lyapunov function, with the help of the finite time control technology, is used to obtain a virtual vehicle state variable that quickly converges in a finite time. control input β _i (t); The actual control input solving module is used to construct the Lyapunov function again according to the error system obtained by the nonlinear transformation in the state constraint module, combined with the virtual control input obtained in the virtual control input solving module, and further obtain the actual control according to the finite time control technology. input u _i (t); The vehicle power control signal solving module is used to obtain the vehicle acceleration and deceleration control signal according to 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 is accelerated. Decelerate, and further obtain the acceleration and deceleration execution command signal for realizing the safe following distance according to the acceleration and deceleration control signal. 2. a kind of vehicle platoon state constraint finite time control system according to claim 1, is characterized in that, actual control input u _i (t) is:

In the formula, k ₁ represents the spacing error adjustment coefficient caused by the driver's reaction time, k ₂ represents the proportional coefficient of the braking distance and the square of the speed, v _i is the speed of the ith vehicle,

is a constant, m _i is the mass of the i-th vehicle, τ _i is the engine time constant, β _i (t) is the virtual control law, ξ _i is the new error after error transformation,

where g _i (v _i ,v _i-1 ,a _i ) and f _i (v _i ,a _i ) are nonlinear functions of velocity and acceleration, φ _i (t) is a function of time t, ε _i is the error correlation quantity after nonlinear transformation of error e _i (t), z ₂ >0, γ>0 are the actual control law parameters. 3. A vehicle platoon state constraint limited time control method, characterized in that, comprising the following steps: (1) Establish a vehicle platooning system dynamics model, which mainly includes a mathematical model of the secondary vehicle spacing error and a single vehicle dynamics model; (2) Establish the error state variable, convert the dynamic model of the vehicle platoon system to a third-order nonlinear error model, and determine the error state quantity _xi , control input _ui and output quantity yi of the _i -th vehicle in the vehicle platoon system ; (3) Establish a finite-time performance function p _i (t); (4) Perform nonlinear mapping transformation on the secondary inter-vehicle distance error between the i-th vehicle and the i-1-th vehicle in the system according to e _i (t)=f(ε _i )p _i (t), the nonlinear function f( ε _i ) is a function of ε _i (t), and ε _i (t) is the error correlation quantity after nonlinear transformation of error e _i (t); (5) Build a virtual control law β _i (t) about the finite-time performance function in the virtual control input solving module of the vehicle platoon state-constrained finite-time controller; (6) The actual control input solving module of the vehicle platoon state-constrained finite-time controller obtains the actual control input u _i (t) according to the third-order error model of the system and the virtual control input; (7) The vehicle power control signal solving module obtains the vehicle acceleration and deceleration control signals according to the actual control input u _i (t), and further solves the acceleration and deceleration execution command signals according to the obtained acceleration and deceleration control signals, so as to achieve the target inter-vehicle distance between the vehicle queues. Fast, accurate tracking for a limited time. 4. A vehicle platoon state constraint finite time control method according to claim 3, wherein the finite time performance function is:

where k and λ are optional positive parameters, T is the set fixed convergence time, p _T is the maximum allowable tracking steady-state error, and the established finite-time performance function satisfies: 1) p _i (t)>0; 2 )

3)

Set fixed convergence time

W() is the Lambert W function. 5. A kind of vehicle platoon state constraint finite time control method according to claim 3, is characterized in that, in described step (5), the construction step based on finite time performance function virtual control law is as follows: Based on the nonlinear mapping transformation e _i (t)=f(ε _i )p _i (t) performed in step (4), where

The first-order derivative of the mapping transformation is performed to obtain the relationship between ε _i (t) and e _i (t); The virtual control input β _i (t) is introduced, and the error coordinate transformation is performed again, so that ξ _i (t)=e _i (t)-β _i (t), and ξ _i is the new error after coordinate transformation; The Lyapunov function is selected to determine the virtual control law β _i (t) and the control law parameters to stabilize the vehicle platoon closed-loop control system. 6 . The method for controlling a vehicle platoon state with limited time constraints according to claim 3 , wherein in the step (2), the state variables of the vehicle platoon system dynamics model include the distance between adjacent vehicles in the vehicle platoon, the distance between adjacent vehicles in the vehicle platoon, and the The speed and acceleration of the bicycles in the queue, the control input is the expected target acceleration of the bicycle, and the state variables of the error model after nonlinear transformation include the distance between adjacent vehicles in the queue, the first derivative function of the distance error, and the second derivative of the distance error. function, the control input is still the desired target acceleration of the bicycle. 7. A kind of vehicle platoon state constraint finite time control method according to claim 3, is characterized in that, establishing vehicle platoon system dynamics model, mainly comprises vehicle secondary vehicle spacing error mathematical model and single vehicle dynamics model, vehicle 2 The mathematical model of the second-vehicle spacing error is expressed as: d _i =x _i-1 -x _i -L _i -S (1) In the formula, d _i is the distance error between adjacent vehicles, _xi (i=1,2,...,n) is the position of the i-th vehicle, Li is the body length of the _i -th vehicle, S is the safe parking distance, Satisfy

k ₁ represents the spacing error adjustment coefficient caused by the driver's reaction time, k ₂ represents the proportional coefficient between the braking distance and the square of the speed, and v _i (i=1,2,...,n) is the speed of the i-th vehicle; The bicycle dynamics model is expressed as:

In the formula, a _i (i=1,2,...,n) is the acceleration of the i-th vehicle, m _i is the mass of the i-th vehicle, and _Fe,i represents the driving force generated by the engine, which satisfies

τ _i is the engine time constant, _ui is the control input,

represents the air resistance, ρ is the air density, A is the cross-sectional area of the vehicle, C is the air resistance coefficient, F _f,i = m _i gfcosθ is the rolling resistance, g is the acceleration of gravity, f is the rolling resistance coefficient, and θ is the road gradient , F _g,i = m _i gsinθ is the resistance caused by gravity, D _i is the unknown external disturbance caused by strong wind and uneven road surface, and the disturbance is assumed to be bounded.

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