Trajectory tracking control method based on data-driven h-infinity fuzzy value iteration

Abstract

The present application relates to the technical field of automobile steer-by-wire system control, in particular to a trajectory tracking control method based on data-driven fuzzy value iteration. In view of the nonlinearity and uncertainty of the steer-by-wire (SBW) system, a local linear model of the SBW system is constructed by using T-S fuzzy technology. By introducing a reference signal, a fuzzy augmented tracking system is constructed. Then, a fuzzy discount coupled algebraic Riccati equation based on Hamilton-Jacobi-Bellman equation is derived. Further, a data-driven fuzzy tracking value iteration (VI) algorithm is designed to solve the tracking control problem of the system through online iteration. The outstanding feature of the algorithm is that it completely eliminates the dependence on system dynamics information, and it can realize closed-loop trajectory tracking control without an initial stable control strategy. The method can be widely applied to intelligent driving, automatic driving steering control and other fields, and is particularly suitable for scenes where the system model is uncertain and control initialization is difficult.

Description

Technical Field

[0001] This invention relates to the field of automotive electronic control technology, specifically to a data-driven... The fuzzy value iterative algorithm-based trajectory tracking control scheme for steering systems is particularly suitable for nonlinear trajectory tracking control of steer-by-wire (SBW) systems. Background Technology

[0002] As a revolutionary alternative to traditional steering mechanisms, steer-by-wire systems replace the mechanical connection between the steering wheel and the front wheels with an electrical connection, providing enhanced driving safety, comfort, and energy efficiency. SBW systems and related technologies are widely considered key enabling technologies for autonomous driving and significant advancements in future intelligent transportation systems.

[0003] However, the elimination of mechanical connections and the increased reliance on sensor actuators introduce significant nonlinearities and uncertainties. Actuator saturation, hysteresis, and friction are the main sources of nonlinearity, posing significant challenges to the design of robust and accurate controllers. While various nonlinear control techniques have been proposed to address these issues, they are not specifically designed for the structural characteristics and critical requirements of SBW systems.

[0004] Tracking control has received widespread attention in various fields, including DC-DC Boost converter systems and single-link robotic arms. The main objective of tracking control is to ensure that the system output follows a reference trajectory while meeting specified performance criteria. However, current research on tracking control typically relies on two main components: a feedback term obtained from the solution of the coupled algebraic Riccati equations and a feedforward term obtained by solving auxiliary differential equations. These methods usually require complete dynamic information or an initial stable control strategy, which is difficult to obtain in practical systems, greatly limiting their practical applicability.

[0005] Reinforcement learning, as a data-driven approach, provides an effective way to solve optimal control problems. Based on the principles of reinforcement learning, RL methods iteratively measure the approximate optimal performance of the corresponding control mechanism, thereby reducing the need for precise dynamic knowledge. However, for SBW systems with nonlinearity and uncertainty, how to solve the tracking control problem using ADP methods in the absence of system dynamics and an initial stable control strategy remains a technical challenge that current technologies have not yet adequately addressed. Summary of the Invention

[0006] The purpose of this invention is to provide a data-driven... A trajectory tracking control scheme for steering systems based on fuzzy value iterative algorithm is proposed, which solves the problems of strong dependence on system dynamics information and the need for initial stable control strategies in existing technologies.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] Data-driven The trajectory tracking control method based on fuzzy value iteration includes the following steps:

[0009] S1. Use TS fuzzy technology to establish a local linear model of the steer-by-wire system, and combine it with reference signals to construct a fuzzy augmented tracking system (FATS);

[0010] S2. Derive the fuzzy discounted differential Riccati equation (FDMRE) using the Hamilton-Jacobi-Bellman equation;

[0011] S3, Design based on data-driven principles The fuzzy tracking value iterative (VI) algorithm solves the tracking control problem through online iteration;

[0012] S4. Prove the asymptotic mean square stability (AMSS) of the closed-loop FATS in the Lyapunov sense and the convergence of the value iteration algorithm;

[0013] S5: Apply the optimal control strategy obtained from the solution to the steer-by-wire system to achieve trajectory tracking control.

[0014] Preferably, the steps for constructing the TS fuzzy model of the steer-by-wire system in step S1 include:

[0015] S1.1: Establish the dynamic model of the steer-by-wire system

[0016] The nonlinear dynamic equations of the steer-by-wire system are as follows:

[0017] ;

[0018] in For the steering wheel angle, For rotational inertia, The viscous damping coefficient is... As an uncertain factor, It is a nonlinear frictional torque. To correct the torque, For motor constants, The rack force acting on the steering rack, For current;

[0019] During the control process, external disturbances and inherent nonlinear characteristics introduce significant uncertainties into the system model; to simplify controller design, and Integrate into lumped disturbance term Thus, the following simplified dynamic equation is obtained:

[0020] ;

[0021] Among them, the nonlinear uncertainty term satisfy ,and These are known constants; here Indicates motor torque;

[0022] Define the state vector as ,in , The system can be represented as:

[0023] ;

[0024] in,

[0025] ;

[0026] S1.2: Constructing the TS fuzzy model

[0027] The Takagi-Sugeno fuzzy modeling method is used to model nonlinear terms. By performing local linear approximation, the following fuzzy rules are constructed:

[0028] if yes , yes ,……,and yes ,So

[0029] ;

[0030] in Indicates the rule index. It is related to the premise variable Associated fuzzy sets, where ; , and It is a system matrix. In the fuzzy model of the steer-by-wire system (TS), the relationship with the first... The local output matrix associated with the fuzzy rules, the variable vector is defined as follows: ;

[0031] By applying the fuzzy mixing mechanism, the overall fuzzy model can be obtained as follows:

[0032] ;

[0033] Where the normalized weight function Product with fuzzy membership degree Defined as:

[0034] ;

[0035] in, express In fuzzy sets The degree of membership in the equation; therefore, for all ,have and ;therefore, ,and ;

[0036] S1.3: Constructing a fuzzy augmentation system containing a reference signal

[0037] Define the reference trajectory as ;

[0038] in and The reference trajectory state and output are respectively: and It is a constant;

[0039] Based on the fuzzy system and the reference signal, an extended state vector is introduced. and extended output vector , obtain and rules The corresponding Overall Extended Fuzzy Tracking System (OFATS);

[0040] Control rules :

[0041] if yes , yes yes ,So

[0042] ;

[0043] ;

[0044] in,

[0045] ;

[0046] The tracking error is: ,in, , ;

[0047] Next, a set of fuzzy control strategies is constructed, each strategy being associated with its corresponding performance function and value function; the overall control strategy is designed as follows:

[0048] Control rules :if yes , yes ,and yes ,So ,in and They represent the rules respectively. Control gain and interference gain;

[0049] By combining OFATS with a control strategy, the closed-loop OFATS is obtained as follows: ,in, , $, , , ;

[0050] The above system's first The fuzzy discount performance function and value function of the rule are defined as follows:

[0051] ;

[0052] ;

[0053] in and It is a positive definite weighted matrix, and ;constant It is the discount factor, and This is the expected level of disturbance attenuation.

[0054] Preferably, the derivation of the fuzzy discount coupled algebraic Riccati equation in step S2 includes:

[0055] Based on Bellman optimization theory, construct the discount performance function and value function:

[0056] ;

[0057] ;

[0058] in As a discount factor, This represents the interference attenuation level.

[0059] Preferably, the data driving in step S3 Fuzzy tracking value iterative algorithms include:

[0060] Transform FDCARE into the fuzzy differential matrix Riccati equation (FDMRE):

[0061] .

[0062] Preferably, this algorithm can achieve optimal control without requiring an initial stable control strategy; the value iteration algorithm is implemented as follows:

[0063] (1) Data collection: For the quadratic form of the defined value function, Differentiating it yields the standard form:

[0064] ;

[0065] in, ;

[0066] ;

[0067] The following collection formula can be obtained:

[0068] ;

[0069] Define the following matrix:

[0070] ;

[0071] ;

[0072] ;

[0073] ;

[0074] (2) Strategy evaluation:

[0075] ;

[0076] (2) Strategy Improvement:

[0077] .

[0078] Preferably, the proposed algorithm is used for closed-loop system testing. Performance and convergence proof;

[0079] Define the Lyapunov function as:

[0080] ;

[0081] The system satisfies the requirements through analysis. Performance metrics:

[0082] ;

[0083] Convergence:

[0084] If there is an additional solution for the data collection method, and the additional solution is defined as... Therefore:

[0085] ;

[0086] Subtracting the above equation from the standard equation, we get

[0087] ;

[0088] Will and Substituting into the above formula, we get:

[0089] ;

[0090] Right now ;

[0091] because We can obtain c=0, and thus the following result:

[0092] ;

[0093] From the above formula, we can obtain... and Therefore, we can obtain the convergence result:

[0094] ,

[0095] ,

[0096] .

[0097] Preferably, the practical application of the control scheme in the online steering system includes:

[0098] Front wheel steering angle control is achieved through a steering motor, force feedback is provided by a feedback motor, and the electronic control unit executes the proposed value iteration algorithm to achieve trajectory tracking control without model information.

[0099] The beneficial effects of this invention include:

[0100] 1. The steering trajectory tracking control method of this application, based on the TS fuzzy method, establishes a practical state-space model for SBW systems with nonlinearity and uncertainty. Then, the fuzzy discounted coupled algebraic Riccati equation for FATS is derived using Bellman optimization theory. This provides a basis for solving closed-loop FATS... The tracking problem provides a structured approach. It achieves true data-driven control without requiring any information from the system dynamics model.

[0101] 2. The steering trajectory tracking control method of this application is developed through data-driven... Fuzzy tracking value iterative algorithm to solve closed-loop FATS Fuzzy tracking control problem. This algorithm can achieve closed-loop trajectory tracking without requiring dynamic information and an initial stable control strategy.

[0102] 3. The steering trajectory tracking control method of this application proves the convergence of the proposed data-driven algorithm and the stability of the closed-loop FATS using Lyapunov theory. An asymptotic mean square stability criterion is established, and the data-driven stability is rigorously proven. Convergence of the fuzzy tracking value iterative algorithm. Attached Figure Description

[0103] Figure 1 This is a block diagram of the overall control system structure according to an embodiment of the present invention;

[0104] Figure 2 This is a data-driven embodiment of the present invention. Flowchart of the fuzzy tracking control value iterative algorithm;

[0105] Figure 3 Embodiments of the present invention , , and Convergence result graph;

[0106] Figure 4 This is the trajectory tracking result of the system state output and the reference state output in an embodiment of the present invention. Detailed Implementation

[0107] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0108] Implementation Example 1: System Modeling and FATS Construction (see appendix of the manual) Figure 1 Overall control system structure block diagram;

[0109] First, establish the dynamic model of the SBW system. Define the state vector as... ,in The system can be represented as:

[0110] ;

[0111] in For nonlinear uncertainty terms, satisfying .

[0112] Using the TS fuzzy modeling method, nonlinear terms The analysis is performed over multiple linear regions. The fuzzy inference rules of the system are defined as follows:

[0113] Control rules :if equal , equal ,…, equal ,So

[0114] ,

[0115] Through the fuzzy mixing mechanism, the overall fuzzy model is obtained as follows:

[0116] .

[0117] Example 2: Design of a value iteration algorithm (see appendix to the instruction manual). Figure 2 Flowchart of a data-driven H∞ fuzzy tracking control value iterative algorithm;

[0118] For fuzzy systems and reference signals, an augmented state vector is introduced. and augmented output vector Thus, the Overall Augmented Fuzzy Tracking System (OFATS) was obtained.

[0119] Design data-driven The fuzzy tracking value iterative algorithm is as follows:

[0120] Initialization: from any initial control gain and Begin by setting the initial iteration values. Choose a sufficiently small positive real number Repeat the process until convergence;

[0121] Data collection: using control strategies and exploring noise Collect data;

[0122] Strategy evaluation: based on the equation Estimate conditions and update ;

[0123] Strategy Improvement: Through renew , and ;

[0124] Output: Stable control gain , and .

[0125] Example 3: Stability and convergence analysis, see appendix of the instruction manual. Figure 3 Figure showing the convergence results for P, K, L, and γ;

[0126] 1. Prove the asymptotic mean-square stability of the system using Lyapunov theory. The Lyapunov function is chosen as... And prove that the closed-loop system satisfies Stability metrics:

[0127] ;

[0128] 2. Algorithm convergence

[0129] Construct a sequence of value functions This proves that it is monotonically decreasing:

[0130] 3. Monotonicity: ;

[0131] 4. According to the monotone convergence theorem, the sequence converges to the optimal value function. ;

[0132] 5. ;

[0133] 6. ;

[0134] 7. .

[0135] Example 4: Simulation verification, see appendix to the instruction manual. Figure 4 The trajectory tracking results of the system state output and the reference state output;

[0136] Define system state nonlinear terms Assuming Therefore, we can obtain

[0137] ;

[0138] in,

[0139] ;

[0140] ;

[0141] It is a constant. .

[0142] Fuzzy rule 1: If If it equals 0, then .

[0143] Fuzzy rule 2: If equal ,So .

[0144] in, , , , .

[0145] OFATS can be obtained as follows: ;

[0146] in .

Claims

1. Data-driven The trajectory tracking control method based on fuzzy value iteration is characterized by, Includes the following steps: S1: Establish a dynamic model of the steer-by-wire system, and use fuzzy technology to construct a local linear model, and combine it with a preset reference signal to construct a fuzzy augmented tracking system; The fuzzy augmented tracking system includes an expanded state vector. and the Control input under fuzzy rules and interference input and the corresponding matrix of the system , and ; Step S2: Based on the principles of reinforcement learning, construct the first... Fuzzy discount performance function of rule and value function : ； ； in and It is a positive definite weighted matrix, and , , For local output matrix, It is a constant; a constant It is the discount factor, and This is the expected level of disturbance attenuation; Step S3: Derive the fuzzy discounted differential Riccati equation and transform it into the fuzzy differential matrix Riccati equation: ； in, For matrix variables, For iterative index, It is a positive real number; Building a data-driven The fuzzy tracking value iterative algorithm uses online collected data to solve the fuzzy differential matrix Riccati equation to obtain the optimal control strategy; The Fuzzy tracking value iterative algorithms include: (1) Data collection; (2) Strategy evaluation; (3) Strategy improvement; Step S4: Verify the stability and convergence of the closed-loop fuzzy augmented tracking system using Lyapunov functions; Step S5: Apply the optimal control strategy obtained from the solution to the electronic control unit of the steer-by-wire system to drive the steering motor to perform trajectory tracking.

2. The method according to claim 1, characterized in that, The step S1, which establishes the dynamic model of the steer-by-wire system, specifically includes: Construct nonlinear dynamic equations to describe the dynamic relationship between steering wheel angle, moment of inertia, viscous damping coefficient, and motor torque; The nonlinear frictional torque and restoring torque in the system are integrated into a lumped disturbance term; Define a state vector containing the steering wheel angle and its rate of change, and represent the steer-by-wire system in a state-space form containing the system matrix, input matrix, and output matrix.

3. The method according to claim 2, characterized in that, Step S1 utilizes fuzzy techniques to construct a local linear model, specifically employing the Takagi-Sugeno fuzzy modeling method, including: Construct fuzzy inference rules to perform local linear approximation of nonlinear uncertainty terms; For each fuzzy rule, define the corresponding local system matrix, local input matrix, local perturbation matrix, and local output matrix; By using a normalized weighting function to weight and fuse the local models under all fuzzy rules, a fuzzy model of the steer-by-wire system is obtained.

4. The method according to claim 3, characterized in that, The step S1, which involves constructing a fuzzy augmentation tracking system using a preset reference signal, specifically includes: Introduce a reference trajectory equation that includes a reference state and a reference output; Define an extended state vector composed of the steering-by-wire system state vector and the reference state vector; Define an extended output vector, which is a combination of the output vector of the steering-by-wire system and the reference output vector; Construct a fuzzy augmented tracking system that includes tracking error, where the tracking error is the difference between the actual system output and the reference output.

5. The method according to claim 1, characterized in that, Step S2 specifically includes: Define a fuzzy control strategy, which includes feedback control gain and disturbance suppression gain; Construct a value function, which is the integral of a weighted quadratic function of the extended state vector, control input, and disturbance input over an infinite time domain; A fuzzy discounted differential Riccati equation is established, which describes the balance between the time derivative of the value function and the system Hamiltonian function.

6. The method according to claim 1, characterized in that, In step S3 The initialization process of the fuzzy tracking value iterative algorithm includes: Initialize the iteration index, initial control gain matrix, and initial interference gain matrix; Probe noise is introduced into the initial control strategy to stimulate the dynamic characteristics of the system in the early stages of iteration.

7. The method according to claim 6, characterized in that, In step S3 The fuzzy tracking value iterative algorithm includes a data collection step: Based on the structure of the value function, construct data relationships that do not depend on the parameters of the system dynamics model; Within a preset time interval, the system acquires expanded state vectors, control input data, and interference data. Using the Kronecker product operation, a dataset containing state autocorrelation matrix, state-control cross-correlation matrix, and state-disturbance cross-correlation matrix is ​​constructed.

8. The method according to claim 7, characterized in that, In step S3 The iterative process of the fuzzy tracking value iterative algorithm also includes a policy evaluation step and a policy improvement step: Strategy evaluation step: Using the dataset constructed in the data collection step, solve the kernel matrix containing the Riccati matrix variables using the least squares method; Strategy improvement steps: Update the control gain matrix and interference gain matrix based on the solved kernel matrix; The data collection step, policy evaluation step, and policy improvement step are executed repeatedly until the control gain matrix converges.

9. The method according to claim 1, characterized in that, The process of verifying the stability of the closed-loop fuzzy augmented tracking system using the Lyapunov function in step S4 includes: Construct positive definite Lyapunov functions; Set an interference attenuation level target and verify that the impact of external interference on the system tracking error under worst-case conditions is limited to the target range, ensuring the system has... Robust performance; The verification shows that as the number of iterations increases, the value function sequence monotonically decreases and converges to the optimal solution.

10. The method according to claim 1, characterized in that, Step S5 is specifically manifested as follows: The electronic control unit reads vehicle sensor data in real time as the system status. After the electronic control unit runs converged Fuzzy tracking value iterative algorithm to calculate the optimal control input; The steering motor outputs torque according to the optimal control input, overcoming nonlinear friction and road surface interference, so that the front wheel steering angle tracks the preset reference trajectory in real time.

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