Resilient observer-based unified state and fault estimation for nonlinear parabolic PDE systems via fuzzy approach over finite-time interval

With the aid of a resilient fuzzy observer, this study delves into the investigation of finite-time state and fault estimation for parabolic-type nonlinear PDE systems described by fuzzy models with faults and external disturbances. Primarily, a fuzzy-dependent observer is built to offer precise estimations of the states and faults simultaneously. Therein, the fluctuations that exhibit random character are taken into account in the observer gain, which enhances the resiliency of the configured fuzzy observer. Meanwhile, the phenomenon of randomly occurring gain fluctuations is effectively characterized by utilizing a random variable that adheres to the Bernoulli distribution. Subsequently, by employing the Lyapunov stability theory and the integral-based Wirtinger's inequality, a set of adequate criteria is obtained in the form of linear matrix inequalities to ascertain that both the state and fault estimation errors are stable in a finite-time with a gratified extended passivity performance index. In the meantime, the observer gain matrices can be obtained by relying on the developed criteria. Ultimately, the simulation results of the Fisher equation are offered to emphasize the superiority of the developed resilient fuzzy observer-based approach.