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CN108749816B - A method of intelligent vehicle speed regulation using energy dissipation theory - Google Patents

A method of intelligent vehicle speed regulation using energy dissipation theory Download PDF

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CN108749816B
CN108749816B CN201810463553.9A CN201810463553A CN108749816B CN 108749816 B CN108749816 B CN 108749816B CN 201810463553 A CN201810463553 A CN 201810463553A CN 108749816 B CN108749816 B CN 108749816B
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张蕊
马育林
关志伟
刘晓锋
闫光辉
张扬
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Tianjin University of Technology
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Abstract

本发明涉及一种运用能量耗散理论进行智能车辆速度调控的方法，其特征是：利用耗散系统中常用的γ耗散不等式，将智能车辆的速度调控转化成以能量存储函数为优化目标的耗散控制问题，采用基于Backstepping设计的Lyapunov方法，构造保证γ耗散的能量存储函数，通过逐步逼近γ耗散不等式，计算得到车辆速度调控的最优控制律。有益效果：本发明通过将智能车辆的速度调节与控制转化成以能量存储函数为优化目标的耗散控制问题，采用Lyapunov直接法代替求解复杂的Riccati方程，通过逐步逼近γ耗散不等式，得到车辆速度调控的最优控制律。

Figure 201810463553

The invention relates to a method for controlling the speed of an intelligent vehicle by using the energy dissipation theory. For the dissipation control problem, the Lyapunov method based on Backstepping design is used to construct an energy storage function that guarantees γ dissipation, and the optimal control law for vehicle speed regulation is obtained by gradually approximating the γ dissipation inequality. Beneficial effects: The present invention transforms the speed regulation and control of the intelligent vehicle into a dissipation control problem with an energy storage function as the optimization objective, uses the Lyapunov direct method to replace the complex Riccati equation, and obtains the vehicle by gradually approximating the γ dissipation inequality. Optimal control law for speed regulation.

Figure 201810463553

Description

Method for regulating and controlling speed of intelligent vehicle by using energy dissipation theory
Technical Field
The invention relates to the field of intelligent vehicles, in particular to a method for regulating and controlling the speed of an intelligent vehicle by using an energy dissipation theory.
Background
In the face of the high-rise automobile keeping quantity of cities in China, the urban traffic problem is difficult to solve in a short time by advocating travel tools such as walking, bicycles, public transportation and new energy automobiles. As an important carrier of an intelligent transportation system, the intelligent vehicle technology is still an effective means for solving the problems of driving safety and road traffic capacity. In particular, the intelligent driving system based on the optimized design can perform performance evaluation of safety, comfort, economy and the like by means of norm or index. For example, a vehicle multi-target coordinated adaptive cruise control method (ZL 200810224248.0) integrates an inter-vehicle distance error and a vehicle speed error into H∞The norm is taken as a safety performance index; h for expecting control cost and disturbance2The norm is taken as a comfort performance index; a fuzzy chaotic control system for vehicle transverse dynamics and a control method (ZL 201310373691.5) thereof regard a Lyapunov index of a driving track error and an initial track error as a manipulation performance index. However, the above optimization method requires constructing Hamilton (Hamilton) function, and using Riccati equation and model to predict the resultTo optimize the control law, the solution process is complex and satisfies many constraints. For example, a cost or cost function weights all control inputs, and all weighting functions are stable; solving the Riccati equation requires ensuring convergence of the solution.
The dissipation system reflects the energy loss characteristic in the system motion process, the norm can be adopted to reflect the gain of the system in the signal transmission process, and the Lyapunov method can be adopted to design the energy sum of the whole system comprising a forward channel and a feedback loop. Therefore, by means of a gamma dissipation inequality commonly used in a dissipation system, the speed regulation and control of the intelligent vehicle are converted into a dissipation control problem which takes an energy storage function as optimization and adjustment, and the acceleration, the speed, the displacement and the corresponding weight factor of the current vehicle are obtained through solving, so that the speed of the intelligent vehicle is better regulated and controlled. For example, an electric vehicle speed control method (ZL201410408955.0), an intelligent vehicle speed control management system and implementation method (ZL201310283519.0) and the like are provided with accurate and effective vehicle critical speed and vehicle speed control database information including displacement, speed, acceleration, weight factors and the like.
Disclosure of Invention
The invention aims to overcome the defects of the technology and provides a method for regulating and controlling the speed of an intelligent vehicle by using an energy dissipation theory, wherein the optimal control law for regulating and controlling the speed of the vehicle is obtained by gradually approaching a gamma dissipation inequality.
In order to achieve the purpose, the invention adopts the following technical scheme: a method for regulating and controlling the speed of an intelligent vehicle by applying an energy dissipation theory is characterized by comprising the following steps: the method comprises the following steps of converting speed regulation and control of an intelligent vehicle into a dissipation control problem with an energy storage function as an optimization target by utilizing a commonly used gamma dissipation inequality in a dissipation system, constructing the energy storage function for ensuring gamma dissipation by adopting a Backstepping-based Lyapunov method, and calculating to obtain an optimal control law of vehicle speed regulation and control by gradually approaching the gamma dissipation inequality, wherein the method comprises the following specific steps:
(1) establishing a gamma dissipation performance criterion of an intelligent vehicle speed regulation and control system, so that an energy storage function and a control law thereof meet the gamma dissipation performance from external input disturbance d to control cost z:
Figure BDA0001661493510000021
in particular, when d is 0, v is the desired vehicle speeddThe designed speed regulation law satisfies limt→∞|v-vd|＝0；
(2) According to the control cost z in the step (1), defining a dissipation inequality that a smooth and derivable energy storage function meets the above criteria:
Figure BDA0001661493510000022
in the formula, vehicle input variables
Figure BDA0001661493510000039
Vehicle output variable
Figure BDA00016614935100000310
Wherein p and m are representations of different dimensions of real numbers R,
║·║Uand ║ & ║YRespectively, L defined on U and Y2A norm;
(3) adopting a Backstepping-based candidate Lyapunov function as a mathematical expression of the energy storage function according to the energy storage function defined in the step (2)
Figure BDA0001661493510000031
In the formula, x is a group,
Figure BDA0001661493510000032
respectively the running displacement and the speed of the intelligent vehicle at a certain moment, and correspondingly, xd，
Figure BDA0001661493510000033
Are respectively series ofIntegrating expected running displacement with vehicle speed and normal number lambda1，λ2，λ3The weight factors are respectively the weight factors of each item in the formula and are used for balancing the proportion of each item;
(4) according to the mathematical expression described in step (3), a vehicle dynamics model having the following general form
Figure BDA0001661493510000034
Wherein x is a state vector of the vehicle,
Figure BDA0001661493510000035
d is the external input disturbance vector, u is the control vector, function g1And g2Satisfy the matching condition
Figure BDA0001661493510000036
The cost function z is solved through the energy storage function;
(5) the vehicle speed regulation control law according to the step (4) has the following general solution
u＝α(x)+β(x)
Wherein the first component α (x) is the stability control law of the vehicle speed regulation system, and defines the sliding mode surface function s
Figure BDA0001661493510000037
Wherein, c1>0, and
Figure BDA0001661493510000038
according to the arrival and stable condition of the sliding form surface, the method can obtain
Figure BDA0001661493510000041
(6) Deriving the energy storage function V over time according to the second component of the generic solution of step (5):
Figure BDA0001661493510000042
(7) the method according to the step (6), only order
Figure BDA0001661493510000043
The gamma dissipation performance criterion of the intelligent vehicle speed regulation system can be ensured;
(8) obtaining an intelligent vehicle speed regulation control law u by deriving the step (3) according to the method in the step (4) -the step (7)
Figure BDA0001661493510000044
The optimality of the intelligent vehicle speed regulation control law in the step (5) can be solved by approximation about (2) by utilizing the currently common quadratic optimal control.
Has the advantages that: according to the method, the speed regulation and control of the intelligent vehicle are converted into the dissipation control problem with an energy storage function as an optimization target, a Lyapunov direct method is adopted to replace the solving of a complex Riccati equation, and the optimal control law of vehicle speed regulation is obtained by gradually approaching a gamma dissipation inequality.
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FIG. 1 is a block diagram of the system design of the present invention;
FIG. 2A is a graph comparing vehicle displacement curves;
FIG. 2B is a comparison of vehicle speed profiles;
FIG. 2C is a graph comparing vehicle acceleration profiles;
FIG. 3 is a schematic diagram of the variation in traction of a vehicle resulting from the application of the present invention;
fig. 4 is a schematic diagram of the energy consumption of a vehicle obtained by applying the present invention.
Detailed Description
The following detailed description of the preferred embodiments will be made in conjunction with the accompanying drawings.
Referring to the drawings in detail, the embodiment provides a method for regulating and controlling the speed of an intelligent vehicle by using an energy dissipation theory, and the method is characterized in that: the method comprises the following steps of converting speed regulation and control of an intelligent vehicle into a dissipation control problem with an energy storage function as an optimization target by utilizing a commonly used gamma dissipation inequality in a dissipation system, constructing the energy storage function for ensuring gamma dissipation by adopting a Backstepping-based Lyapunov method, and calculating to obtain an optimal control law of vehicle speed regulation and control by gradually approaching the gamma dissipation inequality, wherein the method comprises the following specific steps:
(1) establishing a gamma dissipation performance criterion of an intelligent vehicle speed regulation and control system, so that an energy storage function and a control law thereof meet the gamma dissipation performance from external input disturbance d to control cost z:
Figure BDA0001661493510000051
in particular, when d is 0, v is the desired vehicle speeddThe designed speed regulation law satisfies limt→∞|v-vd|＝0；
(2) According to the control cost z in the step (1), defining a dissipation inequality that a smooth and derivable energy storage function meets the above criteria:
Figure BDA0001661493510000052
in the formula, vehicle input variables
Figure BDA0001661493510000053
Vehicle output variable
Figure BDA0001661493510000054
Wherein p and m are representations of different dimensions of real numbers R,
║·║Uand ║ & ║YRespectively, L defined on U and Y2A norm;
(3) adopting a Backstepping-based candidate Lyapunov function as a mathematical expression of the energy storage function according to the energy storage function defined in the step (2)
Figure BDA0001661493510000061
In the formula, x is a group,
Figure BDA0001661493510000062
respectively the running displacement and the speed of the intelligent vehicle at a certain moment, and correspondingly, xd，
Figure BDA0001661493510000063
Respectively the expected running displacement and the vehicle speed of the system and the normal number lambda1，λ2，λ3The weight factors are respectively the weight factors of each item in the formula and are used for balancing the proportion of each item;
(4) according to the mathematical expression described in step (3), a vehicle dynamics model having the following general form
Figure BDA0001661493510000064
Wherein x is a state vector of the vehicle,
Figure BDA0001661493510000065
d is the external input disturbance vector, u is the control vector, function g1And g2Satisfy the matching condition
Figure BDA0001661493510000066
The cost function z is solved through the energy storage function;
(5) the vehicle speed regulation control law according to the step (4) has the following general solution
u＝α(x)+β(x) (5)
Wherein the first component α (x) is the stability control law of the vehicle speed regulation system, and defines the sliding mode surface function s
Figure BDA0001661493510000067
Wherein, c1>0, and
Figure BDA0001661493510000068
according to the arrival and stable condition of the sliding form surface, the method can obtain
Figure BDA0001661493510000069
(6) And (4) calculating a time derivative of the energy storage function V by adopting a matching method according to the second component of the general solution in the step (5):
Figure BDA0001661493510000071
(7) the method according to the step (6), only order
Figure BDA0001661493510000072
The gamma dissipation performance criterion of the intelligent vehicle speed regulation system can be ensured;
(8) obtaining an intelligent vehicle speed regulation control law u by deriving the step (3) according to the method in the step (4) -the step (7)
Figure BDA0001661493510000073
The optimality of the intelligent vehicle speed regulation control law in the step (5) can be solved by approximation about (2) by utilizing the currently common quadratic optimal control.
Examples are given.
First, as shown in FIG. 1, u and d represent the control input variable and the external disturbance input variable of the speed control system of the controlled vehicle, respectively, and the measurable output variable y mainly comprises the vehicle running displacement x and speed
Figure BDA0001661493510000074
And z is the control penalty of the design. According to the measurement output y, a control input u is obtained by designing a proper energy storage function and a proper vehicle speed regulation law, so thatObtaining L between the external input d and the designed control cost z in the whole vehicle speed control system2The gain is minimum, and the stability of the closed-loop system in the Lyapunov sense can be ensured.
Secondly, according to equation (4), the currently common vehicle longitudinal dynamics equation is changed into the following form:
Figure BDA0001661493510000081
wherein the vehicle state vector
Figure BDA0001661493510000086
Respectively representing vehicle displacement and speed, d is external input disturbance, u is vehicle speed regulation control law, and u ═ F-km- μmg)/m. m represents the mass of the vehicle, kmAnd kdThe coefficient of mechanical resistance and the coefficient of air resistance of the vehicle are respectively, mu is the coefficient of rolling friction of the vehicle, and g is the acceleration of gravity.
It is then time-differentiated according to the energy storage function (3) given herein:
Figure BDA0001661493510000082
substituting (12) the intelligent vehicle speed regulation control law (10) to obtain the vehicle speed regulation control law
Figure BDA0001661493510000083
Wherein, let c1＝2,λ1＝6,λ2＝0.5,λ 32 in the formula (13)
Figure BDA0001661493510000084
And is
Figure BDA0001661493510000085
Finally, the Hamilton function of the system is defined as follows
Figure BDA0001661493510000091
I.e., the gamma dissipation performance criterion (1) can be satisfied.
As shown in fig. 2A-2C, the values of the specific parameters of the intelligent vehicle are as follows: m is 1500, kd＝0.3，km＝140，μ＝0.02，vdes25 m/s. The external disturbance takes the sign function of the change in vehicle acceleration,
Figure BDA0001661493510000092
i.e. the acceleration change is bounded. γ is 1, which is an initial value of a parameter in the intelligent vehicle speed control law, and γ is 0.05, which is an approximate value obtained by a common quadratic optimization method. Through the tracking control simulation of the given vehicle speed, the response curve in the graph shows that the supply rate gamma is gradually reduced by using an optimization method, and the tracking precision of the intelligent vehicle speed regulating and controlling system on the given signal can be quickly and effectively improved.
As shown in fig. 3, the adopted vehicle longitudinal dynamics model (11) does not consider modeling actuators such as a brake/accelerator, but directly applies an intelligent vehicle speed control law to the vehicle, so that a part of traction force changes in fig. 3 have negative values. According to the interaction relationship between the traction force and the braking force, the following conditions are provided: when the tractive effort is negative, it can be considered that the braking force is active. Therefore, the energy consumed by the whole process of the intelligent vehicle should include the sum of the work done by the traction force and the work done by the braking force, and the calculation of Σ | F | is simplified in the simulation. As can be seen from fig. 3, the traction force obtained by using the supply rate γ of 0.05 during the tracking process of the smart car is smoother than the change when γ is 1, so that the energy consumption value 429380J obtained by simplifying the calculation is 5% less than 453820J calculated when γ is 1, as shown in fig. 4. The vehicle speed control method is obtained on the premise that the loss of actuating mechanisms such as a brake/accelerator and the like is not considered, so that the vehicle speed control effect is very obvious.
The above detailed description of the method for implementing fleet collaborative driving by means of semi-physical simulation technology is illustrative and not restrictive with reference to the embodiments, and several embodiments can be enumerated within the limited scope, so that variations and modifications thereof without departing from the general concept of the present invention shall fall within the protection scope of the present invention.

Claims (2)

1.一种运用能量耗散理论进行智能车辆速度调控的方法，其特征是：利用耗散系统中常用的γ耗散不等式，将智能车辆的速度调控转化成以能量存储函数为优化目标的耗散控制问题，采用基于Backstepping设计的Lyapunov方法，构造保证γ耗散的能量存储函数，通过逐步逼近γ耗散不等式，计算得到车辆速度调控的最优控制律，具体步骤如下：1. A method of using the energy dissipation theory to control the speed of an intelligent vehicle, characterized in that: using the γ dissipation inequality commonly used in the dissipation system, the speed control of the intelligent vehicle is converted into a consumption that takes the energy storage function as an optimization target. The Lyapunov method based on Backstepping design is used to construct an energy storage function that guarantees γ dissipation, and the optimal control law for vehicle speed regulation is calculated by gradually approximating the γ dissipation inequality. The specific steps are as follows: (1)建立智能车辆速度调控系统的γ耗散性能准则，使能量存储函数及其控制律满足从外界输入扰动d到控制代价z的γ耗散性能：(1) Establish the γ dissipation performance criterion of the intelligent vehicle speed control system, so that the energy storage function and its control law satisfy the γ dissipation performance from the external input disturbance d to the control cost z:
Figure FDA0001661493500000011
Figure FDA0001661493500000011
 特别地，当d＝0时，对于期望的车速vd，所设计的车速调控律满足limt→∞|v-vd|＝0；In particular, when d=0, for the desired vehicle speed v d , the designed vehicle speed control law satisfies lim t→∞ |vv d |=0; (2)根据步骤(1)的控制代价z，定义光滑、可导的能量存储函数满足上述准则的耗散不等式：(2) According to the control cost z in step (1), define a smooth and differentiable energy storage function that satisfies the dissipation inequality of the above criteria:
Figure FDA0001661493500000012
Figure FDA0001661493500000012
 式中，车辆输入变量
Figure FDA0001661493500000013
车辆输出变量
Figure FDA0001661493500000014
In the formula, the vehicle input variable
Figure FDA0001661493500000013
vehicle output variable
Figure FDA0001661493500000014
 其中，p，m为实数R不同维度的表示，Among them, p, m are the representations of different dimensions of the real number R, ||·||U和||·||Y分别表示定义在U和Y上的L2范数；||·|| U and ||·|| Y represent the L 2 norm defined on U and Y, respectively; (3)根据步骤(2)定义的能量存储函数，采用基于Backstepping的候选Lyapunov函数作为能量存储函数的数学表达式(3) According to the energy storage function defined in step (2), the candidate Lyapunov function based on Backstepping is used as the mathematical expression of the energy storage function
Figure FDA0001661493500000015
Figure FDA0001661493500000015
 式中，x，
Figure FDA0001661493500000016
分别是智能车辆某一时刻的行驶位移与车速，相应的，xd，
Figure FDA0001661493500000021
分别为系统期望的行驶位移与车速，正常数λ1，λ2，λ3分别为式中每项的权重因子，用于平衡各项所占的比重；where, x,
Figure FDA0001661493500000016
are the driving displacement and vehicle speed of the intelligent vehicle at a certain moment, correspondingly, x d ,
Figure FDA0001661493500000021
are the expected driving displacement and vehicle speed of the system, respectively, and the normal numbers λ 1 , λ 2 , and λ 3 are the weight factors of each item in the formula, which are used to balance the proportion of each item; (4)根据步骤(3)描述的数学表达式，针对具有如下通用形式的车辆动力学模型(4) According to the mathematical expression described in step (3), for the vehicle dynamics model with the following general form
Figure FDA0001661493500000022
Figure FDA0001661493500000022
 式中，x是车辆的状态向量，
Figure FDA0001661493500000023
d是外界输入扰动向量，u是控制向量，函数g1和g2满足匹配条件
Figure FDA0001661493500000024
代价函数z通过上述的能量存储函数进行求解；where x is the state vector of the vehicle,
Figure FDA0001661493500000023
d is the external input disturbance vector, u is the control vector, and the functions g 1 and g 2 satisfy the matching conditions
Figure FDA0001661493500000024
The cost function z is solved by the above energy storage function; (5)根据步骤(4)所述车速调节控制律具有如下通解(5) According to step (4), the vehicle speed regulation control law has the following general solution u＝α(x)+β(x)u=α(x)+β(x) 其中，第一分量α(x)为车速调控系统的镇定控制律，定义滑模面函数sAmong them, the first component α(x) is the stabilization control law of the vehicle speed control system, which defines the sliding mode surface function s
Figure FDA0001661493500000025
Figure FDA0001661493500000025
 其中，c1>0，且
Figure FDA0001661493500000026
where c 1 >0, and
Figure FDA0001661493500000026
 根据滑模面到达与稳定条件，可得According to the arrival and stability conditions of the sliding surface, we can get
Figure FDA0001661493500000027
Figure FDA0001661493500000027
 (6)根据步骤(5)所述通解的第二分量，对能量存储函数V求时间的导数：(6) According to the second component of the general solution described in step (5), the time derivative is calculated for the energy storage function V:
Figure FDA0001661493500000031
Figure FDA0001661493500000031
 (7)根据步骤(6)所述方法，只有令(7) According to the method described in step (6), only make
Figure FDA0001661493500000032
Figure FDA0001661493500000032
 才能保证智能车辆速度调控系统的γ耗散性能准则；Only then can the γ dissipation performance criterion of the intelligent vehicle speed control system be guaranteed; (8)根据步骤(4)—(7)所述方法对(3)求导，得到智能车速调节控制律u(8) derivation of (3) according to the method described in steps (4)-(7) to obtain the intelligent vehicle speed regulation control law u
Figure FDA0001661493500000033
Figure FDA0001661493500000033
 2.根据权利要求1所述的运用能量耗散理论进行智能车辆速度调控的方法，其特征是：所述步骤(5)的智能车速调节控制律的最优性可利用目前常用的二次型最优控制对其进行关于(2)的逼近求解。2. the method that utilizes energy dissipation theory to carry out intelligent vehicle speed regulation and control according to claim 1, is characterized in that: the optimality of the intelligent vehicle speed regulation control law of described step (5) can utilize the quadratic type commonly used at present The optimal control performs an approximate solution to (2).
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