Synthesis of Fault Tolerant Control Laws

Abstract

The FTCSMP can be modelled by stochastic differential equations and can be viewed as a general hybrid system. The research in this area can be broadly classified into two categories: The first concerns with deriving conditions for the existence of controllers. The second deals with properties of FTCSMP such as stability, controllability and observability. The major portion of the book has been focused on studying system properties, in particular, the stochastic stability. The exponential stability in the mean square was studied in [168]. Stochastic stability of FTCSMP in noisy environment was considered in [128], for multiple failure process in [129], and with parameter uncertainties in [124]. In this chapter, a state feedback controller for FTCSMP will be designed in both noise-free and noisy environments. The matrix maximum principle [3] is used to minimize an equivalent deterministic cost function.