Robust Dynamic Actuator Failure Compensation Control of Nonlinear Systems via Cooperative Interaction Design

This article studies fault-tolerant resilient control (FTRC) problems for uncertain Takagi–Sugeno fuzzy systems when subjected to additive actuator faults and/or malicious injections on control input signals. The effects of faults and malicious injections are modeled by unknown bounded signals. The signals are produced by any finite-
$L_{2}$
-gain dynamical system and a Lipschitz and derivable function with respect to states, so that the considered fault model contains some reported ones as special cases. By employing the available state and input data, a function, which is equivalent to a fictitious dynamical system comprising the information about compensation errors for unknown actuator faults, is presented. Then, based on the virtual system, a novel actuator failure compensator (AFC) with the structure of dynamic feedbacks is proposed, so that the compensation capability is improved via cooperative interaction designs between the virtual dynamical systems and closed-loop systems. Furthermore, through the equivalence class and Lyapunov theories, it is proved that the presented robust dynamic AFC-based fuzzy controller ensures the asymptotic convergence of system states to zero. Different from the existing FTRCs, good transient performance is guaranteed, even in the presence of unforeseen actuator faults. Two illustrative examples verify the effectiveness of the presented method.