Optimal Adaptive Control for Nonlinear Uncertain Systems

How to achieve a compromise between the accuracy of parameter estimation and the robustness of system is still a challenging task in adaptive control field. To address this issue, a novel optimal adaptive control (OAC) strategy is proposed for a model reference adaptive control (MRAC) system with uncertain dynamics. To realize this purpose, a low-pass filter operation is first employed for the linearized system to derive the parameter estimation error information. Then, a cost function concerning the tracking error and estimation error is established. Then, the MIT rule is introduced to reconstruct a new optimal adaptive law driven by the parameter estimation error information. In this framework, both the tracking error and parameter estimation error can converge to zero simultaneously. The asymptotic stability of the closed-loop system is analyzed in terms of the Lyapunov theorem. Finally, comparative simulation results are provided to exemplify the effectiveness of the proposed control method.