Optimal tracking control method for multi-mode automotive suspension system

Abstract

The invention discloses an optimal tracking control method for a multi-mode automotive suspension system, and belongs to the technical field of intelligent control of vehicles. Aiming at the problems of dynamic jump, strong uncertainty and multi-actuator cooperative control of an automotive suspension system in various driving modes, the invention provides a robust tracking control framework based on interval type-2 fuzzy Markov jump system modeling and combined with a distributed minimum-maximum game and integral reinforcement learning. The method comprises the following steps: firstly, considering unknown nonlinear dynamics, external pavement excitation and parameter random jump existing in a suspension system, and modeling the system as an interval type-2 fuzzy Markov jump system; secondly, aiming at the actual constraint that the dynamic part of the system is unknown and only output information can be obtained, constructing a distributed control framework; according to the method, the tracking performance, the closed-loop stability and the multi-actuator cooperation efficiency of the suspension system can be guaranteed under the environment that the system modes are randomly switched and the dynamic uncertainty is high, and the smoothness, the safety and the robustness of vehicle driving are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of vehicle intelligent control technology, and in particular to an optimal tracking control method for a multimodal vehicle suspension system. Background Technology

[0002] The automotive suspension system is a key component affecting a vehicle's ride comfort, handling stability, and safety. Traditional passive and semi-active suspensions, limited by fixed mechanical characteristics or limited adjustment capabilities, struggle to maintain optimal performance under varying driving conditions and road surface excitations. Active suspensions, by outputting control forces in real time through force actuators, offer the possibility of achieving a leap in performance; however, their core challenge lies in designing effective control strategies to address the multiple uncertainties inherent in the system itself and in the environment.

[0003] In actual vehicle operation, the dynamics of the suspension system can change abruptly due to load variations, component aging, or mode switching (such as comfort / sport mode). Such behavior is well-suited for stochastic modeling using Markov jump systems. Simultaneously, the system's strong nonlinearity, unmodeled dynamics, and external stochastic excitations constitute deep uncertainties, which traditional Type I fuzzy systems struggle to handle. Interval Type II fuzzy systems introduce additional degrees of freedom through membership functions, providing a more robust framework for characterizing and encapsulating such uncertainties. However, research on deeply integrating interval Type II fuzzy logic with Markov jump systems to construct high-fidelity suspension models and design controllers based on them is still insufficient, especially in complex scenarios where the system's dynamic parameters are unknown and multiple actuators need to work collaboratively. Significant gaps remain in both the theoretical framework and control algorithms in these cases.

[0004] At the control architecture level, modern automotive suspensions are typically equipped with multiple independent actuators, and their coordinated control can be abstracted as a multi-person decision-making problem. Traditional optimal control methods usually assume that the system model is precisely known and optimized for a single control objective, making them difficult to directly apply to the aforementioned game scenario with multi-source uncertainty and multiple control inputs. Differential game theory provides a natural framework for this, and its Nash equilibrium solution can guarantee the collective optimality of the strategies of all participants while considering individual interest conflicts or coordination. However, existing suspension control research based on game theory mostly still relies on precise, centralized system models and often requires full-state feedback that is difficult to obtain directly, limiting its deployment and application in actual automotive embedded systems.

[0005] To reduce reliance on precise models, reinforcement learning, especially integral reinforcement learning, has attracted widespread attention in the field of adaptive optimal control due to its "model-independent" and online learning characteristics. It can learn the optimal strategy online using system input-output data without requiring an explicit mathematical model of the system's internal dynamics. However, existing research on applying reinforcement learning to suspension control has significant limitations: first, it largely focuses on single-actuator systems or highly simplified coupled models, failing to delve into the distributed learning and decision-making problems of multiple actuators under game-theoretic relationships; second, it fails to combine it with interval-type II fuzzy Markov jump system models that can accurately describe the system's multimodal transitions and strong uncertainties; and third, most algorithms rely on full-state feedback, lacking effective solutions for the prevalent output feedback constraints.

[0006] In summary, existing technologies struggle to simultaneously address the four core challenges faced by automotive active suspension systems: multimodal stochastic transitions, deep fuzzy uncertainty, multi-actuator game-theoretic optimization, and output feedback constraints. Therefore, developing a distributed, model-independent, and robust optimal tracking control method capable of operating in this complex environment is of urgent theoretical necessity and significant engineering application value for improving the overall performance and adaptability of intelligent vehicle chassis systems. Summary of the Invention

[0007] The main technical problem to be solved by this invention is: for automotive suspension systems with multimodal jumps, strong uncertainties, and multi-actuator coordination requirements, under the conditions that the dynamic part of the system is unknown, only output feedback can be obtained, and external disturbances exist, how to establish a system model that can simultaneously characterize random jumps and fuzzy uncertainties, and design a distributed, low-model-dependency optimal tracking control strategy, so that each actuator can work together in mutual game to drive the suspension system state to robustly track the ideal reference trajectory, and strictly guarantee the asymptotic stability and disturbance suppression performance of the closed-loop system.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] An optimal tracking control method for a multimodal vehicle suspension system includes the following steps:

[0010] S1: Establish an interval type II fuzzy Markov jump system model, considering a car suspension system. Car suspension model:

[0011] ;

[0012] in For vehicle body displacement, For tire displacement, For road surface displacement, The pitch angle, For control input;

[0013] Define state vector The above model can be converted into a state-space form:

[0014] ;

[0015] Its system matrix is:

[0016] ;

[0017] ;

[0018] System parameters follow Markov process The transition probability matrix of the jump is:

[0019] ;

[0020] S2: Constructing a tracking error system and performance metrics for multiplayer games:

[0021] Define reference trajectory:

[0022] ;

[0023] Constructing composite states With composite output Define tracking error:

[0024] ;

[0025] in, ;

[0026] Define the player (actuator) The cost function is:

[0027] ;

[0028] in Including decision-makers The set of control inputs from other participants;

[0029] S3: Design a distributed minimax game control framework:

[0030] Construct a cost function that includes input from a virtual adversary:

[0031] ;

[0032] in Input for the virtual opponent, This is the disturbance suppression level parameter. and The weight matrix is ​​symmetric and positive definite.

[0033] The control objective is to find the minimum-maximum policy:

[0034] ;

[0035] S4: Solving the Riccati equation for a type-II fuzzy differential game in an interval:

[0036] ;

[0037] The optimal control law and the virtual opponent strategy are as follows:

[0038] ;

[0039] in This is the optimal gain matrix;

[0040] S5: Design an offline parallel distributed integral reinforcement learning algorithm:

[0041] When the system dynamics are fully known, the following iterative update solution is used. ;

[0042] ;

[0043] in:

[0044] ;

[0045] S6: Design an online parallel distributed integral reinforcement learning algorithm:

[0046] When the dynamic part of the system is unknown or there is model uncertainty, an online data-driven integral reinforcement learning method is adopted. By collecting system input and output data in real time, the control strategy is iteratively updated without prior knowledge of the system matrix. , and Specifically, it includes the following steps:

[0047] S6.1: Constructing Data-Driven Learning Equations:

[0048] S6.2: Define the data acquisition matrix and its vectorized representation;

[0049] S6.3: Construct a system of linear equations and solve it;

[0050] S6.4: Online iterative update strategy;

[0051] S6.5: Convergence and stability guarantees.

[0052] Preferably, in step S1, considering the vehicle suspension system, a fuzzy model is adopted as follows:

[0053] Fuzzy rules :if yes , yes ,..., yes ,but:

[0054] ;

[0055] in, Let be the system state vector. For the first The control input of an actuator For the system output vector, As a prerequisite variable; It is an interval type II fuzzy set;

[0056] It is the total number of fuzzy rules. It is the number of prerequisite variables. For a finite set A continuous-time Markov process taking values ​​from 0 to 1 has transition probabilities that satisfy:

[0057] ;

[0058] in, and ;

[0059] Through fuzzy mixing, the following overall fuzzy system is derived:

[0060] ;

[0061] in:

[0062] .

[0063] Preferably, in step S2, the reference trajectory system is designed as follows:

[0064] ;

[0065] The initial state is set to .

[0066] Preferably, in step S6.1, based on the system dynamic equations:

[0067] ;

[0068] By defining the relationship between the state increment and the cost function, we obtain the data-driven learning equation:

[0069] .

[0070] Preferably, in step S6.2, to facilitate online solution, the above equations are transformed into linear parameterized form, and the following data matrices and vectors are defined:

[0071] State difference matrix:

[0072] ;

[0073] State autocorrelation integral matrix:

[0074] ;

[0075] Control-state cross-integral matrix:

[0076] ;

[0077] Virtual control - state cross-integral matrix:

[0078] .

[0079] Preferably, in step S6.3, the above matrix is ​​substituted into the learning equation to obtain a system of linear equations:

[0080] ;

[0081] in For the reason and The coefficient matrix formed; The parameter to be determined includes and ; The vector on the right is... Composed of equal items;

[0082] When the data volume meets When the total number of parameters is equal to the total number of parameters, the solution is obtained using the least squares method:

[0083] .

[0084] Preferably, in step S6.4, based on the solution obtained... Extract the updated matrix This is then used for the calculation of the control law at the next time step. Steps S6.1 to S6.3 are repeated until the parameters converge.

[0085] Preferably, in step S6.5, Lyapunov analysis is used to prove that the strategy sequence generated by the online algorithm... The solution converges to the optimal solution during the iteration process. Furthermore, the closed-loop system maintains bounded stability for the actual preset time.

[0086] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0087] 1. This application employs an interval-type II fuzzy Markov jump system for modeling, effectively characterizing the modal stochastic jumps and deep uncertainties of automotive suspension under varying operating conditions, significantly enhancing the model's ability to describe complex dynamics and its adaptability. The constructed distributed minimax game framework transforms the multi-actuator cooperative problem into a non-cooperative differential game, enabling each actuator to achieve global performance optimization based on local information, thus improving the system's scalability and decision-making autonomy. The integral reinforcement learning method used, through online interactive data-driven strategy optimization, significantly reduces the dependence on precise mathematical models, enhancing the control system's autonomous learning and robustness in unknown dynamics and environments. The designed output feedback control structure, combined with rigorous theoretical proof, ensures the asymptotic stability of the closed-loop system under disturbances and the preset disturbance suppression level, providing a reliable theoretical guarantee for engineering practice. Attached Figure Description

[0088] Figure 1 This is a schematic diagram of the process of the present invention;

[0089] Figure 2 This is a diagram of a car suspension system according to the method of the present invention;

[0090] Figure 3 The following is a detailed diagram of the simulation results of the method of the present invention. Detailed Implementation

[0091] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0092] Please see Figure 1-3 The present invention provides a technical solution:

[0093] An optimal tracking control method for a multimodal vehicle suspension system includes the following steps:

[0094] S1: Establish an interval type II fuzzy Markov jump system model, considering a car suspension system. Car suspension model:

[0095] ;

[0096] in For vehicle body displacement, For tire displacement, For road surface displacement, The pitch angle, To control the input; the system parameters are defined as shown in Table 1:

[0097] ;

[0098] Define state vector The above model can be converted into a state-space form:

[0099] ;

[0100] Its system matrix is:

[0101] ;

[0102] ;

[0103] System parameters follow Markov process The jump parameters are shown in Table 2:

[0104] ;

[0105] The Markov transition probability matrix is:

[0106] ;

[0107] To address the system's nonlinearity, two interval type-2 (IT2) fuzzy rules are used for modeling:

[0108] Rule 1: If yes ,but:

[0109] ;

[0110] Rule 2: If yes ,but:

[0111] ;

[0112] The membership function is designed as follows:

[0113] ;

[0114] The corresponding weight function is:

[0115] ;

[0116] S2: Constructing a tracking error system and performance metrics for multiplayer games:

[0117] Define reference trajectory:

[0118] ;

[0119] Constructing composite states With composite output Define tracking error:

[0120] ;

[0121] in, ;

[0122] Define the player (actuator) The cost function is:

[0123] ;

[0124] in Including decision-makers The set of control inputs from other participants;

[0125] S3: Design a distributed minimax game control framework:

[0126] Construct a cost function that includes input from a virtual adversary:

[0127] ;

[0128] in Input for the virtual opponent, This is the disturbance suppression level parameter. and The weight matrix is ​​symmetric and positive definite.

[0129] The control objective is to find the minimum-maximum policy:

[0130] ;

[0131] S4: Solving the Riccati equation for a type-II fuzzy differential game in an interval:

[0132] ;

[0133] The optimal control law and the virtual opponent strategy are as follows:

[0134] ;

[0135] in This is the optimal gain matrix;

[0136] S5: Design an offline parallel distributed integral reinforcement learning algorithm:

[0137] When the system dynamics are fully known, the following iterative update solution is used. ;

[0138] ;

[0139] in:

[0140] ;

[0141] Offline algorithm process:

[0142] Initialization: Set the convergence threshold Initial solution ;

[0143] Iterative calculation: for each fuzzy rule Modality and players .

[0144] Then, the following iterative update method is used to solve the problem. :

[0145] ;

[0146] Convergence criterion: If Then stop; otherwise Return to the iterative calculation step;

[0147] Output: Optimal solution obtained .

[0148] The optimal gain can be obtained through this offline algorithm. .

[0149] S6: Design an online parallel distributed integral reinforcement learning algorithm:

[0150] When the dynamic part of the system is unknown or there is model uncertainty, an online data-driven integral reinforcement learning method is adopted. By collecting system input and output data in real time, the control strategy is iteratively updated without prior knowledge of the system matrix. , and ,

[0151] Online algorithm flow:

[0152] Set convergence threshold Given initial parameters ;

[0153] Data collection: within a time interval Internally, the system status is collected. Control input Virtual control input Data, with a sampling period of 0.01s;

[0154] Construct a data matrix;

[0155] Specifically, the following steps are included:

[0156] S6.1: Constructing Data-Driven Learning Equations:

[0157] S6.2: Define the data acquisition matrix and its vectorized representation;

[0158] S6.3: Construct a system of linear equations and solve it;

[0159] S6.4: Online iterative update strategy;

[0160] S6.5: Convergence and stability guarantees.

[0161] In step S1, considering the car suspension system, the following fuzzy model is used:

[0162] Fuzzy rules :if yes , yes ,..., yes ,but:

[0163] ;

[0164] in, Let be the system state vector. For the first The control input of an actuator For the system output vector, As a prerequisite variable; It is an interval type II fuzzy set;

[0165] It is the total number of fuzzy rules. It is the number of prerequisite variables. For a finite set A continuous-time Markov process taking values ​​from 0 to 1 has transition probabilities that satisfy:

[0166] ;

[0167] in, and ;

[0168] Through fuzzy mixing, the following overall fuzzy system is derived:

[0169] ;

[0170] in:

[0171] .

[0172] In step S2, the reference trajectory system is designed as follows:

[0173] ;

[0174] The initial state is set to .

[0175] Define the actuators for the three actuators. The cost function is:

[0176] ;

[0177] Among them, the weight matrix is ​​selected. .

[0178] In step S6.1, based on the system dynamic equations:

[0179] ;

[0180] By defining the relationship between the state increment and the cost function, we obtain the data-driven learning equation:

[0181] .

[0182] In step S6.2, to facilitate online solution, the above equations are transformed into linear parameterized form, and the following data matrices and vectors are defined:

[0183] State difference matrix:

[0184] ;

[0185] State autocorrelation integral matrix:

[0186] ;

[0187] Control-state cross-integral matrix:

[0188] ;

[0189] Virtual control - state cross-integral matrix:

[0190] .

[0191] In step S6.3, the above matrix is ​​substituted into the learning equation to obtain a system of linear equations:

[0192] ;

[0193] in For the reason and The coefficient matrix formed; The parameter to be determined includes and ; The vector on the right is... Composed of equal items;

[0194] When the data volume meets When the total number of parameters is equal to the total number of parameters, the solution is obtained using the least squares method:

[0195] .

[0196] Get the updated parameters .

[0197] In step S6.4, based on the solution obtained... Extract the updated matrix This is then used for the calculation of the control law at the next time step. Steps S6.1 to S6.3 are repeated until the parameters converge.

[0198] like If the iteration stops, it stops; otherwise, iterates on.

[0199] In step S6.5, Lyapunov analysis is used to prove that the policy sequence generated by the online algorithm... The solution converges to the optimal solution during the iteration process. Furthermore, the closed-loop system maintains bounded stability for the actual preset time.

[0200] To verify the effectiveness of the optimal tracking control method for multimodal vehicle suspension systems proposed in this invention, Figure 2 The automobile suspension system shown is the controlled object in the simulation experiment. The system parameters are set according to Table 2, and the symbols of each physical quantity are explained in Table 1. The simulation results are as follows: Figure 3 As shown in the figure. The results show that the control method designed in this invention, based on interval type II fuzzy Markov jump system modeling, distributed minimax game, and integral reinforcement learning, can enable the system output to accurately track a given reference trajectory while ensuring that the control input is smooth and bounded. This result demonstrates the effectiveness of the method in handling system modal jumps, uncertainties, and multi-actuator cooperative control problems; the closed-loop system exhibits good tracking performance and stability.

[0201] The above description of the embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. An optimal tracking control method for a multimodal vehicle suspension system, characterized in that, Includes the following steps: S1: Establish an interval type II fuzzy Markov jump system model, considering a car suspension system. Car suspension model: ； in For vehicle body displacement, For tire displacement, For road surface displacement, The pitch angle, For control input; Define state vector The above model can be converted into a state-space form: ； Its system matrix is: ； ； System parameters follow Markov process The transition probability matrix of the jump is: ； S2: Constructing a tracking error system and performance metrics for multiplayer games: Define reference trajectory: ； Constructing composite states With composite output Define tracking error: ； in, ; Define the player (actuator) The cost function is: ； in Including decision-makers The set of control inputs from other participants; S3: Design a distributed minimax game control framework: Construct a cost function that includes input from a virtual adversary: ； in Input for the virtual opponent, This is the disturbance suppression level parameter. and The weight matrix is ​​symmetric and positive definite. The control objective is to find the minimum-maximum policy: ； S4: Solving the Riccati equation for a type-II fuzzy differential game in an interval: ； The optimal control law and the virtual opponent strategy are as follows: ； in This is the optimal gain matrix; S5: Design an offline parallel distributed integral reinforcement learning algorithm: When the system dynamics are fully known, the following iterative update solution is used. ; ； in: ； S6: Design an online parallel distributed integral reinforcement learning algorithm: When the dynamic part of the system is unknown or there is model uncertainty, an online data-driven integral reinforcement learning method is adopted. By collecting system input and output data in real time, the control strategy is iteratively updated without prior knowledge of the system matrix. , and Specifically, it includes the following steps: S6.1: Constructing Data-Driven Learning Equations: S6.2: Define the data acquisition matrix and its vectorized representation; S6.3: Construct a system of linear equations and solve it; S6.4: Online iterative update strategy; S6.5: Convergence and stability guarantees.

2. The optimal tracking control method for a multimodal vehicle suspension system according to claim 1, characterized in that, In step S1, considering the vehicle suspension system, a fuzzy model is adopted as follows: Fuzzy rules :if yes , yes ,..., yes ,but: ； in, Let be the system state vector. For the first The control input of an actuator For the system output vector, As a prerequisite variable; It is an interval type II fuzzy set; It is the total number of fuzzy rules. It is the number of prerequisite variables. For a finite set A continuous-time Markov process taking values ​​from 0 to 1 has transition probabilities that satisfy: ； in, and ; Through fuzzy mixing, the following overall fuzzy system is derived: ； in: 。 3. The optimal tracking control method for a multimodal vehicle suspension system according to claim 1, characterized in that, In step S2, the reference trajectory system is designed as follows: ； The initial state is set to .

4. The optimal tracking control method for a multimodal vehicle suspension system according to claim 1, characterized in that, In step S6.1, based on the system dynamic equations: ； By defining the relationship between the state increment and the cost function, we obtain the data-driven learning equation:

5. The optimal tracking control method for a multimodal vehicle suspension system according to claim 4, characterized in that, In step S6.2, to facilitate online solution, the above equations are transformed into linear parameterized form, and the following data matrices and vectors are defined: State difference matrix: ； State autocorrelation integral matrix: ； Control-state cross-integral matrix: ； Virtual control - state cross-integral matrix: 。 6. The optimal tracking control method for a multimodal vehicle suspension system according to claim 5, characterized in that, In step S6.3, the above matrix is ​​substituted into the learning equation to obtain a system of linear equations: ； in For the reason and The coefficient matrix formed; The parameter to be determined includes and ; The vector on the right is... Composed of equal items; When the data volume meets When the total number of parameters is equal to the total number of parameters, the solution is obtained using the least squares method: 。 7. The optimal tracking control method for a multimodal vehicle suspension system according to claim 6, characterized in that, In step S6.4, based on the solution obtained... Extract the updated matrix This is then used for the calculation of the control law at the next time step. Steps S6.1 to S6.3 are repeated until the parameters converge.

8. The optimal tracking control method for a multimodal vehicle suspension system according to claim 7, characterized in that, In step S6.5, Lyapunov analysis is used to prove that the strategy sequence generated by the online algorithm... The solution converges to the optimal solution during the iteration process. Furthermore, the closed-loop system maintains bounded stability for the actual preset time.

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