Fuzzy Fault Tolerant Control of a Bacterial Growth Process Using a Multiple Lyapunov Function

This paper presents the problem of actuator fault estimation and fault-tolerant control (FTC) of a biological process using Takagi–Sugeno fuzzy formulation. The goal is to ensure the desired outputs tracking even if the time-varying actuator faults occur. We propose to use a proportional multi-integral (PMI) observer to estimate both the time-varying actuator faults and the state of system. The reconstructed faults are used to reconfigure the nominal controller. As a nominal control, we use a fuzzy linear quadratic integral (LQI) law. To ensure the global asymptotic convergence of the PMI observer and to improve the compensation speed of faults, we propose to use the multiple Lyapunov function by introducing a convergence rate. Sufficient conditions in terms of linear matrix inequalities (LMIs) are developed. The obtained results show that, the proposed approach is successfully applied to the problem of actuator fault-tolerant control of a bacterial growth process.