$H∞$ Fuzzy Tracking Control Design for Nonlinear Active Fault Tolerant Control Systems

This paper studies the problem of $H∞$ fuzzy tracking control design for nonlinear active fault tolerant control systems based on the Takagi and Sugeno fuzzy model. Two random processes with Markovian transition characteristics are introduced to model the system component fault process and the fault detection and isolation decision process used to reconfigure the control law, respectively. The random behavior of the FDI process is conditioned on the fault process state. The parallel distributed compensation scheme is employed for the control design. As a result, a closed-loop fuzzy system with two Markovian jump parameters is obtained. Based on a stochastic Lyapunov function, a sufficient condition for stochastic stability of the closed-loop fuzzy system with a guaranteed $H∞$ model reference tracking performance is first derived. A linear matrix inequality approach to the control design is then developed to reduce the effect of the external disturbance and reference input on tracking error as small as possible. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method.