Stochastic analysis and synthesis of active fault tolerant control systems

Modern technological systems rely on sophisticated control functions to meet increased performance requirements. For these systems, Fault Tolerant Control Systems (FTCS) need to be developed. FTCS can be broadly classified into active and passive. Active FTCS rely on a Fault Detection and Isolation (FDI) process to monitor system performance, and to detect and isolate faults. The dynamic behavior of active FTCS can be modelled by stochastic differential equations, because faults are random in nature, and the FDI decisions are non-deterministic.; The main objective for this dissertation is to study and validate important practical issues of real-time FTCS by theoretical developments and extensive simulation examples. To achieve this objective, several FTCS models have been developed. These models take into consideration practical aspects of the system to be controlled, performance deterioration in FDI algorithms, and the design of reconfiguration mechanisms in real-time environments.; The first issue considered in the dissertation concerns with the practical issues of the system to be controlled. This involves: the inclusion of the environment noises, the handling of multiple faults in different system components, and the effect of actuators saturation.; As for the deterioration in the FDI performance, the dissertation focus on three main FDI imperfections, namely: detection delays, errors in detection and isolation, and inaccurate post-fault estimated system parameters.; Then, the dissertation proposes several design approaches for a reconfigurable fault tolerant control law. The controller is first synthesized in noise-free environment, then results are extended to design a reconfigurable controller in noisy environment.; The dissertation adopts the Lyapunov second (direct) method to characterize the behavior of FTCS without explicit solution of the stochastic differential equations. A prime focus for the dissertation is the stochastic stability of FTCS. In particular, exponential stability in the mean square and almost sure asymptotic stability. The weak infinitesimal operator and the supermartingale property of a stochastic Lyapunov function are employed to derive conditions for stochastic stability of FTCS.; All theoretical results were validated by several simulation examples. Therefore, researchers and industrial experts will appreciate the combination of practical issues and mathematical theory. Control engineers will benefit from the obtained results by extending work to different application areas.