H ∞ Differential Game of Nonlinear Half-Car Active Suspension via Off-Policy Reinforcement Learning

Gang Wang (), Jiafan Deng, Tingting Zhou and Suqi Liu
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Gang Wang: Guangxi Key Laboratory of Manufacturing System & Advanced Manufacturing Technology, Guilin University of Electronic Technology, Guilin 541004, China
Jiafan Deng: Guangxi Key Laboratory of Manufacturing System & Advanced Manufacturing Technology, Guilin University of Electronic Technology, Guilin 541004, China
Tingting Zhou: Guangxi Key Laboratory of Manufacturing System & Advanced Manufacturing Technology, Guilin University of Electronic Technology, Guilin 541004, China
Suqi Liu: Guangxi Key Laboratory of Manufacturing System & Advanced Manufacturing Technology, Guilin University of Electronic Technology, Guilin 541004, China

Mathematics, 2024, vol. 12, issue 17, 1-18

Abstract: This paper investigates a parameter-free H ∞ differential game approach for nonlinear active vehicle suspensions. The study accounts for the geometric nonlinearity of the half-car active suspension and the cubic nonlinearity of the damping elements. The nonlinear H ∞ control problem is reformulated as a zero-sum game between two players, leading to the establishment of the Hamilton–Jacobi–Isaacs (HJI) equation with a Nash equilibrium solution. To minimize reliance on model parameters during the solution process, an actor–critic framework employing neural networks is utilized to approximate the control policy and value function. An off-policy reinforcement learning method is implemented to iteratively solve the HJI equation. In this approach, the disturbance policy is derived directly from the value function, requiring only a limited amount of driving data to approximate the HJI equation’s solution. The primary innovation of this method lies in its capacity to effectively address system nonlinearities without the need for model parameters, making it particularly advantageous for practical engineering applications. Numerical simulations confirm the method’s effectiveness and applicable range. The off-policy reinforcement learning approach ensures the safety of the design process. For low-frequency road disturbances, the designed H ∞ control policy enhances both ride comfort and stability.

Keywords: nonlinear active suspension; H ? differential game; off-policy reinforcement learning; HJI equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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