Active fault-tolerant fuzzy control design of nonlinear model tracking with application to chaotic systems

The active fault-tolerant control (FTC) design problem for nonlinear model tracking based on the Takagi and Sugeno (T–S) fuzzy model is dealt with. For a nonlinear active FTC system, two random processes with Markovian transition characteristics are introduced to model the system component failure process and the fault detection and isolation (FDI) decision process used to reconfigure the control law, respectively. The random behaviour of the FDI process is conditioned on the failure process state. First, the T–S fuzzy model is employed to exactly represent the FTC system and the nonlinear reference model. A fuzzy controller is used to generate the FDI-decision-dependent control signal. As a result, an error fuzzy system with two Markovian jump parameters is obtained. Then, based on a stochastic Lyapunov function, a linear matrix inequality approach to the fuzzy control design is developed such that the error system is exponentially stable in the mean square and an H∞ model-tracking performance is guaranteed. Finally, the proposed design method is successfully applied to the chaotic model-tracking control between Lorenz system and Rossler system.