Polytopic models for observer and fault-tolerant control designs

Abstract : As systems become more and more complex, the use of nonlinear models for modeling is often unavoidable. However, nonlinear models naturally increase the difficulty of designing state estimation observers, control laws, and fault-tolerant control strategies. In fact, a specific analysis of the nonlinearities is needed to propose appropriate theoretical tools to deal with these problems. An interesting way to avoid analysis of the nonlinearities is by using the polytopic model approach to reduce the complexity of the automatic control problems. The goal of this chapter is to show the interesting properties of polytopic models as well as their eventual limits. By means of pedagogical examples, this chapter shows how polytopic models can be employed to model nonlinear systems. Stability results are also proposed to design a state feedback controller, and observers for state and unknown input estimations. A fault-tolerant control strategy is also proposed based on an appropriate combination of the state feedback law and the proposed unknown input observer. This strategy is applied to the control of the lateral dynamics of a vehicle in the presence of actuator faults in order to illustrate its validity. A rich survey bibliography is also proposed by the authors.