Robust tracking control for nonlinear systems using the fuzzy asynchronous preview control approach

This paper investigates an innovative technology for asynchronous fuzzy preview control (FPC) in nonlinear Markov jump systems (MJS) with time-varying uncertainties and partly unknown transition probabilities using the Takagi-Sugeno (T-S) fuzzy model. It is assumed that the system modes cannot be obtained synchronously by the controller, but instead there is a detector that provides estimated values of the system modes. The proposed asynchronous FPC strategy depending on the detector mode considers time-changing uncertainties and previewable target signals. The asynchronous controller integrates a fuzzy feedback controller, a fuzzy preview controller, and an integrator to address the tracking control problem of target signals. The research constructs a T-S fuzzy augmented error model (AEM) using the error system method and state augmentation technique. Subsequently, the asynchronous FPC design challenge is transformed into a feedback stabilization problem of the AEM. Employing Lyapunov function and LMI techniques, the study derives sufficient conditions for the stability of the AEM in the form of a set of LMIs, presenting the design method of the asynchronous FPC law. The validity of the results is demonstrated through numerical simulations.