Fault Tolerant Control For Singular Systems And Singular Stochastic Systems

Singular systems is a kind of dynamics systems, which is more general and more natural to represent and to handle practical model such as power systems, economic systems, robotic systems, electrical network systems, astronavigation systems, and so on. The research on singular systems is of important theoretical meaning and practical significance. In the last three decades, there have been a lot of achievements on the stability, controllability, observerability etc, but few efforts were paid to fault tolerant control for singular systems. So there is great space for the development of fault tolerant control for singular systems. In the light of theoretical results of singular systems and that of fault tolerant control for normal systems, we provide a study on the theory of fault tolerant control for singular systems and singular stochastic systems.In practical engineering, except for Lyapunov stability, we paid more attention to the behavior of the systems over a fixed finite time interval, which is called finite- time control problems. An observer-based finite-time control problem for linear singular systems is considered. By using generalized state-observer theory, we design the observer-based state feedback controller, which guarantees that the resultant closed-loop system is impulse free and finite-time stable. Moreover, this paper deals with the finite-time fault-tolerant control problem for uncertain singular system, whose class is with parameter uncertainties and norm bounded. Based on LMI, the integrity design technique with actuators failures is analyzed based on robust fault-tolerant control theory.Based on LMI method, reliable guaranteed cost control and robust H∞fault tolerant control problems are studied, which is a more general actuator failure model. For a class of linear descriptor systems with uncertainty and a given quadratic cost function, we design a reliable guaranteed cost state feedback control law such that, the closed-loop descriptor systems keep regular, impulse-free and stable in the case of actuator failures. Meanwhile, a certain upper bound of a quadratic cost index can be guaranteed. Robust H∞fault-tolerant control of a kind of descriptor delay linear systems with uncertainty and disturbance is studied. In the circumstance of actuator failures, on the basis of generalized Riccati inequality, we obtain the sufficient condition for the systems possessing asymptotical stability against actuator failures and the design method of the controller.It is well known that the Hamliton-Jacobi inequality (HJI) is difficult to resolve, either analytically or numerically. So, the nonlinear system is represented or approximated by a T-S fuzzy model. Actuator failures are classified in terms of extent of failures. Faulty switching system is constructed respect to various classes of actuator failures. A state-feedback-switching controller is designed such that the closed-loop switched system is asymptotically stable with a prescribed H∞performance constraint for arbitrary switching law. Furthermore, we investigate the problem of reliable H∞output tracking control for a class of nonlinear singular system using Takagi-Sugeno (T-S) fuzzy model approach. When the actuator failures cases occurred, a reliable controller is deigned such that the system output follows that of a reference model while satisfying a prescribed H∞performance constraint.The stability and reliable control problems are studied in terms of stability theory for stochastic differential equations. We deal with the problems of robust stochastic stabilization and robust H∞control for Markovian jump nonlinear singular systems with Wiener process via a fuzzy-control approach. The T-S fuzzy model is employed to represent a nonlinear singular system with norm-bounded parameter uncertainties and Markovian jump parameters. Based on stochastic Lyapunov function method, a state feedback fuzzy controller is designed such that the closed-loop fuzzy system is robustly stochastically stable for all admissible uncertainties, and a prescribed performance is achieved. At the same time, we deal with the design problem of robust H∞reliable control for nonlinear singular stochastic systems with actuator failures. Based on LMI techniques, we establish sufficient conditions of existence and design method of robust H∞reliable fuzzy controller. Finally, the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems is studied. A state feedback fuzzy controller is designed such that the resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties as well as different actuator fault cases.