Guaranteed Cost Control For A Class Of Large-scale System Based On T-S Fuzzy Model

With the development of science and technology, the plants to be controlled are becoming larger and more complicated, with high degree of nonlinearity and uncertainty. By utilizing expert experience and language information, analysis, modeling and control problems of many industrial complex plants can be handled effectively by fuzzy control, which otherwise will be very hard by approaches of traditional control theory. In addition, these complex plants can be controlled easily even without exact mathematical models, so fuzzy control has become a popular topic for analysis and design of complex nonlinear systems. Stability is one of the most important performance indexes; however it is not enough for control systems. Linear quadratic performance (guaranteed cost performance) can reflect a lot of performance requirements, so guaranteed cost control of fuzzy large-scale system is studied in this paper. The main contents are as follows:Firstly, based on Lyapunov stability theory, analysis and design of guaranteed cost controller of T-S fuzzy large-scale system is transformed into solving linear matrix inequality by Decentralized Parallel Distributed Compensation (DPDC) fuzzy controller. The sufficient condition on the existence of guaranteed cost controller is derived and performance upper bound of the system is given. To reduce the performance bound, a convex optimization method with linear matrix inequality constraints is proposed. By the technique, the optimal reliable guaranteed cost controller can be designed, which minimizes the cost upper bound of the closed-loop system.Secondly, aiming at the problem of external disturbances uncertainty, a memoryless state feedback controller for a class of fuzzy large-scale system with H_∞and minimal value of cost function constraints is researched by combining guaranteed cost control and H_∞control. The sufficient condition on the existence of H_∞guaranteed cost controller is represented by linear matrix inequality and the optimal guaranteed cost controller is designed.Finally, the problem of reliable guaranteed cost control with state feedback is discussed for a class of fuzzy large-scale system with actuator failures. The sufficient condition of the existence of reliable guaranteed cost controller is put forward and performance upper bound of the system is given. The reliable guaranteed cost controller is designed by a convex optimization method with linear matrix inequality constraints, which minimizes the cost upper bound of the closed-loop system.