Fault tolerant control for uncertain descriptor multi-models with application to wastewater treatment plant

This paper addresses the design of adaptive observer for uncertain descriptor multi-models (MM), affected by unknown inputs (actuator faults) and subject to unknown model parameter variations, in the context of fault tolerant control (FTC) strategy. The FTC strategy contains two parts: the first one aims to estimate the unmeasured states, the actuator faults and the model parameter uncertainties thanks to an observer. In the second part, a control law that takes into account the faults, the uncertainties and the states, provided by the observer, is proposed. This controller is able to compensate the actuator faults even in the presence of parameter uncertainties. The stability of the whole closed-loop system is studied by using the Lyapunov theory. The stability conditions are then expressed in terms of Linear Matrix Inequalities (LMIs). The model parameters are time varying and are involved as polynomials in the dynamic description of the nonlinear system, which corresponds to a more general class of uncertainties in the framework of real process modeling.