Adaptive Control-based on Adaptive Observer for Uncertain Nonlinear Servo Systems

This paper presents a novel approach to the design of an adaptive observer algorithm and corresponding controller for nonlinear servo mechanisms that contain both unknown system states and parameters. The proposed algorithm utilizes an auxiliary matrix to extract the unknown parameter estimation error of the system and design the adaptive law, thus enabling the simultaneous online estimation of the system state and parameters. The convergence of the proposed approach is established, and the persistent excitation condition of the system was then verified online. Based on the estimated values of the adaptive observer, an adaptive controller is designed and shown to achieve convergence and stability of the overall system. Numerical simulations are performed to demonstrate the effectiveness of the proposed observer framework in terms of robustness and tracking performance. The findings of this study have significant implications for the control discipline, offering a new adaptive control approach for nonlinear systems with uncertain parameters.