Dynamic Surface Intelligent Robust Control of Nonlinear Systems With Fixed-Time Sliding-Mode Observer

The high tracking control precision and fast finite-time convergence for nonlinear systems is a significant challenge due to complex nonlinearity and unknown disturbances. To address this challenge, a dynamic surface intelligent robust control strategy with fixed-time sliding-mode observer (DSIRC-SMO) is proposed to improve the tracking control performance in a finite time. First, adaptive fuzzy neural network based on a predictor (P-AFNN) is designed to imitate the complex nonlinearity. In particular, the weight adaptive law is formulated by utilizing the prediction error information, which improves the accuracy of approximating the nonlinear system. Second, the fixed-time sliding-mode observer (SMO) is integrated into the dynamic surface control technique to deal with unknown disturbances and modeling errors in a fixed time. This integration allows for timely updates the dynamic surface using observation information, thereby enhancing the system's anti-interference capability. Then, the fixed-time convergence of SMO is proven. Third, the proposed DSIRC-SMO can be effectively implemented and the finite-time convergence of DSIRC-SMO is proven in detail based on the fixed-time convergence of SMO. Finally, numerical simulation and actual wastewater treatment processes simulation are conducted to validate the effectiveness of DSIRC-SMO.