Quadratic stability and LMIs for tolerance to faults: Fuzzy model predictive control

In this paper, a fault tolerant Fuzzy-Model-Predictive Control (FMPC) with integral action method for a class of nonlinear systems is proposed. Nonlinear systems subject to actuators and/or sensors faults are described by Takagi-Sugeno (T-S) fuzzy model. The objective of this approach is to design a Fault Tolerant Controller (FTC). At each sampling time, MPC solves an optimization to achieve desired set points and control objectives. The feasibility of optimization problem provides the guarantee of the nominal asymptotic stability. However the optimization can be infeasible due to faults. This motivates the development of the proposed approach to recover feasibility with the respect of constraints imposed on control inputs and system states. State vector and faults are estimated by a T-S fuzzy observer. The gains of the fuzzy observer and the pre-stabilized control law are obtained by solving a Linear Matrix Inequality (LMI) derived from the Lyapunov theory. The proposed FTC strategy with Measurable Premise Variables (MPV) is applied to an academic example. Simulation results illustrate the validity of the proposed strategy and its application to FTC.