Reliable Fuzzy Control With Domain Guaranteed Cost For Nonlinear Discrete-time Systems

As is well known, in practical applications, since failures of actuator components often occur in real world, an important reliability requirement for the design of control systems is to guarantee the stability and basic performance of the plant by the designed controller which can tolerate actuator failures. That is, the stability and performance requirements for the closed-loop control systems can be ensured, not only when the systems is operating properly, but also in the presence of actuator failures. So it is significant to research reliable control problem in both theory and practical applications.The main results in the thesis are as follows.(1) The significance of reliable control issue is introduced, both in theory and in applications. And the related development abroad and at home is retrospected briefly.(2) The design method of a reliable fuzzy controller with domain guaranteed cost for nonlinear discrete-time systems with actuator failures is proposed. The Takagi and Sugeno (T-S) fuzzy model is employed to represent the nonlinear systems. A more general failure model is adopted for such actuator failures, which is a function of ideal actuator and consists of the average factor and the failure degree of such actuator. This failure model is more practical, which includes the ideal actuator, the partial failure case and the outage model, respectively. When the initial state of such systems is known, a sufficient criterion for the existence of the reliable fuzzy controller with domain guaranteed cost is derived in the linear matrix inequality (LMI) form, and a parameterized design procedure of such controllers is presented. The designed fuzzy controller not only guarantees the stability of the closed-loop fuzzy system, but also provides a guaranteed cost in the sense of quadratic cost function. Moreover, when the initial state of such systems is unknown, but belongs to a known bounded closed domain (called initial statedomain), polygon domain or ellipsoid domain are considered here, some formulas for the reliable domain guaranteed costs are presented. To decrease the conservatism of the value of the reliable domain guaranteed cost, a design problem of the optimal reliable domain guaranteed cost fuzzy controller is addressed in the sense of minimizing a bound on the reliable domain guaranteed cost via an LMI optimization procedure, which can be solved efficiently using any convex optimization algorithms. A numeric example is given to illustrate the effectiveness of the proposed design methods.(3) The main results of the thesis are concluded, and the subjects of future investigation are proposed.