Optimal H_∞ Adaptive Observer-based Tracking Control of SISO Nonlinear Stochastic Systems with Uncertain Measurement Function and Noise

In this study, the optimal $H_{\infty}$ adaptive observerbased indirect reference tracking control design is proposed for the uncertain single-input-single-output (SISO) nonlinear stochastic system with nonlinear uncertain measurement function and measurement noise. In contrast to conventional observerbased adaptive control designs that assume exact linear output measurement functions and ignore measurement noise, the proposed method embeds adaptive fuzzy logic system (FLS) in indirect adaptive controller and observer to effectively approximate the nonlinear uncertain system function and measurement function, respectively. Then, the optimal $H_{\infty}$ adaptive observerbased tracking control strategy is proposed to efficiently attenuate the effect of the adaptive fuzzy approximation errors, external disturbance and measurement noise on the tracking error and observation error as small as possible via solving a corresponding linear matrix inequalities (LMIs)-constrained optimization problem. Finally, a simulation example is provided to validate the effectiveness of proposed method.