Fault-Tolerant Control For The Dynamical Systems With Multi-indices Constraint

Fault tolerant control is a novel strategy to improve the security and reliability of systems. Its meaning is that dynamical systems can run safely under the acceptable dynamical and stable performances when the faults of dynamic systems occur. Now, the study on fault tolerant control under multi-index constraints is still in primary stage, the results are mainly for normal linear systems. Based on the above consideration, this dissertation consider singular systems, interval systems and non-linear systems, study the fault tolerant control problems for them under the constraints of multiple indexes, propose the satisfactory fault tolerant control for them , deduce the existing conditions and design method of non-fragile satisfactory fault tolerant controller, so as to improve the fault tolerant control theory under multi-index constraints, thus provide a theoretical backbone for its engineering applications. The principal research results and innovations are outlined as follows:(1) The design methods of satisfactory fault tolerant controllers and filters of uncertain singular systems, along with its time-delayed versions, are proposed, comprehensively considering regional pole index, H_∞constraint, variance upper bound and cost guaranteed constraint. We adopt the fault model of actuator, analyze the value ranges of compatible indexes and sufficient conditions for the existing of fault tolerant controller under the constraint of multiple indexes, and a constructive design method of controller is given.(2) The problem of non-fragile fault tolerant control of uncertain linear system and linear system famlies are proposed, with the consideration of uncertainty of controllers. The regional pole index, minimal variance upper bound index and H_∞index are considered comprehensively. Considering compatible theory of these indexes, the design method of non-fragile fault tolerant controller is proposed. Applying neural network to identification, location and diagnosis of faults, with consideration of multi-model reference method, a design method of active fault tolerant control is proposed.(3) Fault tolerant control problems of two class interval systems are presented. Normal and time-delayed interval systems are comprehensively considered, the uncertain systems with fault of actuator are transformed into interval systems, and the fault tolerant problems of uncertain systems are solved with the theory of interval systems. Applying LMI, the inequality problems corresponding to the constraints of performance indexes are transformed to convex optimization problems, and the controller satisfying performance indexes are obtained by solving LMI with Matlab.(4) Fault tolerant control problems under multiple constraints of several kinds of T-S fuzzy systems are studied. One kind of problems is for nonlinear systems described by T-S fuzzy model. The uncertainty of global fuzzy model and the fault of actuator are comprehensively considered, and an idea of fuzzy cost guaranteed fault tolerant control is proposed. The fuzzy control problems are transformed into convex optimization problems with LMI, and an expression of fuzzy H_∞cost guaranteed fault tolerant controller is given. The other kind of problems is about T-S fuzzy singular systems. Under the precondition of quadratic stability, considering H₂ & H_∞performance of system and the design of fault tolerant controller under the constraints of mixed indexes, the quadratic stability, excellent dynamic performance and steady performance of closed-loop fuzzy linear singular systems are ensured .(5) Fault tolerant control of nonlinear systems under multi-index constraints is discussed. In practice, the uncertain parts are norm-bounded, and the nonlinear parts often enjoy the linearly bounded constraints, a design method of fault tolerant controller under multi-index constraints is proposed. H_∞cost guaranteed fault tolerant control of a class of complex uncertain nonlinear systems with time delay is discussed by means of LMI and Lyapunov stability theory. The existing conditions of H_∞cost guaranteed control rules and design methods of controller are given with LMI. The problems of non-fragile H_∞cost guaranteed control of system, when the faults of actuators and perturbations of controller parameters occur, are comprehensively considered in research process. The corresponding existing conditions of non-fragile cost guaranteed fault tolerant control rules, and the design methods of non-fragile cost guaranteed controller are given. The problem of chaos synchronization of chaotic systems with multiple time-delays is discussed by employing the state-feedback controller with memory, and a design approach of nonlinear controller is given for more complicated systems in structure.Finally, the existing problems in this dissertation are discussed, and directions of further researches are pointed out.