In view of the performance requirements (e.g., ride comfort, road holding, and suspension space limitation) for vehicle suspension\nsystems, this paper proposes an adaptive optimal control method for quarter-car active suspension systemby using the approximate\ndynamic programming approach (ADP). Online optimal control lawis obtained by using a single adaptive criticNNto approximate\nthe solution of the Hamilton-Jacobi-Bellman (HJB) equation. Stability of the closed-loop system is proved by Lyapunov theory.\nCompared with the classic linear quadratic regulator (LQR) approach, the proposed ADP-based adaptive optimal control\nmethod demonstrates improved performance in the presence of parametric uncertainties (e.g., sprung mass) and unknown road\ndisplacement. Numerical simulation results of a sedan suspension system are presented to verify the effectiveness of the proposed\ncontrol strategy.
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