Secure fault estimation and resilient fault-tolerant control for nonlinear chaotic systems based on fuzzy intermediate estimator

Under the framework of proportional integral observer, this article investigates the intermediate variable-based fault estimation problem for T–S fuzzy chaotic systems under the influence of actuator faults, external disturbances, deception attacks and gain fluctuations. The first step involves constructing a fuzzy-dependent intermediate variable, followed by the establishment of a fuzzy intermediate variable-based proportional integral estimator to accomplish concurrent estimation of system states and faults. As a next step, leveraging insights from the proportional integral-based fuzzy intermediate estimator, an intermediate estimator-based fuzzy resilient fault-tolerant control is designed to compensate for system faults. Notably, the control gain incorporates fluctuations, which strengthen the resilience of the devised controller. After this, by establishing a suitable Lyapunov–Krasovskii functional, an assortment of sufficient requirements that guarantees the stability and (σ1,σ2,σ3)−χ dissipative performance of the considered system are articulated using linear matrix inequalities. Eventually, simulation results of the Lorenz system are conferred to exemplify the applicability and efficiency of the proposed fuzzy resilient observer-based control design technique.