Optimal H∞ adaptive fuzzy observer-based reference tracking control of nonlinear stochastic systems under uncertain measurement function and noise

The optimal $H_{\infty }$ adaptive fuzzy observer-based indirect reference tracking control designs are proposed in this study for both uncertain SISO and MIMO nonlinear stochastic systems with nonlinear uncertain measurement functions and measurement noise. In contrast to conventional observer-based adaptive control designs that assume exact linear output measurement functions and ignore measurement noise, the proposed method utilizes adaptive fuzzy logic system (FLS) embedded in indirect adaptive controller and observer to effectively cancel the nonlinear uncertain system function and measurement function, respectively. Then, the optimal $H_{\infty }$ adaptive observer-based reference tracking control design strategy is proposed to efficiently minimize the worst-case effect of the adaptive FLS approximation errors, environmental disturbance and output measurement noise on both the reference tracking error and state estimation error of uncertain nonlinear stochastic systems. The study demonstrates that achieving the optimal $H_{\infty }$ adaptive observer-based reference tracking control design strategy requires solving a linear matrix inequalities (LMIs)-constrained optimization problem for the adaptive laws and the $H_{\infty }$ adaptive observer-based reference tracking control law. Finally, we provide two simulation examples to validate the proposed optimal $H_{\infty }$ adaptive observer-based reference tracking control design in SISO and MIMO nonlinear stochastic systems with nonlinear uncertain system functions, measurement functions, environmental disturbance and measurement noise.