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Hysteresis hybrid nonlinear (HHN) systems are characterized by hysteresis nonlinearity and hybrid characteristics, which presents a significant challenge in the development of control strategies. This work aims to examine the optimal control problem of the HHN systems, taking an air spring-magnetorheological suspension (ASMS) system as an example, based on the sum-of-square (SOS) programming. First, the ASMS system is established based on the intergrated model of air spring and magnetorheological damper. Secondly, the SOS approximation theory is adopted to transform the nonlinear functions into sum-of-square polynomials. Then, a relaxed \(L_2\) -gain optimization problem is proposed by adopting \(H_{\infty}\) regulation to find an optimal control strategy for the ASMS system. Finally, the optimal controller is obtained by solving the relaxed \(L_2\) -gain optimization problem. Results indicate a significant enhancement in the dynamic performance of vehicles, as well as an improvement in ride comfort.

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Sum-Of-Square Programming for Magnetorheological Suspension System with  \(H_{\infty}\) Optimal Regulation

  • 会议论文

  • 发表日期：

    2025年

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  • Zhijiang Gao,
  • Lemin Xu,
  • Jing Zhao,
  • Pak Kin Wong

摘要

Hysteresis hybrid nonlinear (HHN) systems are characterized by hysteresis nonlinearity and hybrid characteristics, which presents a significant challenge in the development of control strategies. This work aims to examine the optimal control problem of the HHN systems, taking an air spring-magnetorheological suspension (ASMS) system as an example, based on the sum-of-square (SOS) programming. First, the ASMS system is established based on the intergrated model of air spring and magnetorheological damper. Secondly, the SOS approximation theory is adopted to transform the nonlinear functions into sum-of-square polynomials. Then, a relaxed \(L_2\) -gain optimization problem is proposed by adopting \(H_{\infty}\) regulation to find an optimal control strategy for the ASMS system. Finally, the optimal controller is obtained by solving the relaxed \(L_2\) -gain optimization problem. Results indicate a significant enhancement in the dynamic performance of vehicles, as well as an improvement in ride comfort.