Stabilization of Active Fault Tolerant Control Systems with Imperfect Fault Detection and Diagnosis

Abstract

In active Fault Tolerant Control Systems (FTCSs), a Fault Detection and Diagnosis (FDD) algorithm is used to monitor system performance, detect the occurrence of faults and estimate post-fault system parameters. Usually, estimation techniques employed by the FDD algorithm will provide system parameters with some inaccuracies. As a result, the system to be controlled will include parameter uncertainties. In this paper, exponential stabilization of FTCSs for systems with time-varying unknown-but-bounded parameter uncertainties is considered. In particular, an algorithm that provides a necessary and sufficient condition for exponential stabilization in the mean square is derived. The stabilizing controller is calculated, based on the solutions of matrix Riccati-like algebraic equations. Several interesting special cases are derived from the general result. A numerical example is presented to demonstrate the theoretical developments.