In this study, an adaptive fuzzy inverse optimal control problem is investigated for a class of vehicle active suspension systems. Since active suspension systems have dynamic characteristics of complexities and spring non-linearities, the fuzzy logic systems are utilised to learn the unknown non-linear dynamics. In addition, there exist the constraints of the displacements of the sprung and unsprung masses, vertical vibration speeds, and current intensity in the considered suspension system, therefore, the Barrier Lyapunov functions are introduced into the control design to ensure that the full-state constraints are not overstepped. The inverse optimal control method is adopted by constructing an auxiliary system, which circumvents the assignment of solving a Hamilton–Jacobi–Bellman equation and brings about an inverse optimal controller associated with a meaningful objective functional. Based on Lyapunov stability theory and backstepping recursive design algorithm, a fuzzy adaptive optimal control scheme is developed. It is proved that the proposed control scheme not only guarantees that the vertical vibration of the vehicle is stabilised by the electromagnetic actuator but also achieves the goal of inverse optimality with regard to the cost functional. Finally, the simulation studies check the validity of the presented control strategy.

中文翻译：

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一类具有全状态约束的主动悬架系统的自适应模糊最优控制

在这项研究中，研究了一类车辆主动悬架系统的自适应模糊逆最优控制问题。由于主动悬架系统具有复杂性和弹簧非线性的动态特性，因此模糊逻辑系统可用于学习未知的非线性动力学。此外，在考虑的悬架系统中，还存在着簧上和簧下质量的位移，垂直振动速度和电流强度的约束，因此，将Barrier Lyapunov函数引入控制设计中以确保全状态约束不被超越。通过构造辅助系统，采用逆最优控制方法，它规避了求解Hamilton-Jacobi-Bellman方程的任务，并带来了与有意义的目标函数相关的逆最优控制器。基于Lyapunov稳定性理论和后推递归设计算法，提出了一种模糊自适应最优控制方案。实践证明，所提出的控制方案不仅保证了电磁致动器稳定车辆的垂直振动，而且在成本功能上达到了逆向最优的目的。最后，仿真研究验证了所提出控制策略的有效性。实践证明，所提出的控制方案不仅保证了电磁致动器稳定车辆的垂直振动，而且在成本功能上达到了逆向最优的目的。最后，仿真研究验证了所提出控制策略的有效性。实践证明，所提出的控制方案不仅保证了电磁致动器稳定车辆的垂直振动，而且在成本功能上达到了逆向最优的目的。最后，仿真研究验证了所提出控制策略的有效性。