Adaptive Robust Control For T-S Fuzzy Uncertain Time-Delay Systems

In many practical control systems, we need to establish accurate mathematical models. But, controlled plants vary along with time or the work environment changing; its change rule is always unknown in advance. In the case of the controlled plants varies in the large, we hope that the system still could automatically work in the fine status or near to fine status, and also guarantee the system to be stable and have some basic performances. So it is important to design the adaptive robust controller, not only in theory but also in applications. Furthermore, in the research domain of nonlinear systems, when the controlled plants are modeled by fuzzy systems, the design problem of an adaptive robust controller is converted to that of a fuzzy adaptive robust controller. Noting that the uncertainties often occur in the controlled plants, which may include modeling error, parameter perturbations, fuzzy approximation errors, and external disturbances, etc., and there exist time-delays phenomenon, it is a significant issue to design an adaptive robust controller for uncertain nonlinear systems with time-delays.The main results in the dissertation are as follows:(1) The significance of this paper is introduced, not only in theory but also in applications. And the corresponding development both abroad and at home is recalled briefly.(2) For the nonlinear system, an adaptive robust control method which combines fuzzy model-based control is presented for a class of nonlinear systems with multiple time-delays, parameter uncertainties and external disturbances. The parameter uncertainties are assumed to be norm-bounded with structure properties, which don't satisfy matching conditions. External disturbances satisfying matching conditions are bounded by either continuous functions or high-order nonlinear constraints. The T-S fuzzy model is adopted for the approximate modeling of the nonlinear systems with some unknown uncertainties, and fuzzy-model-based adaptive robust control laws are designed by means of LMI approach for two classes of external disturbances, respectively. The designed controllers can guarantee the state variables of the closed-loop system to converge, globally, uniformly and exponentially, to a ball in the state space by tuning the designed parameters of such controllers. The efficiency of our design method is finally verified by simulation on a chaotic system.(3) The problem of adaptive robust control for T-S fuzzy systems with multiple time-delays, uncertain parameters and external disturbances is studied in this thesis. The uncertain parameters satisfy matching conditions and are norm-bounded. External disturbances also satisfy two different classes of matching conditions which are the same as the above. First, the Takagi and Sugeno (T-S) fuzzy system is employed to approximate the nonlinear system. Furthermore, based on the LMI approach, the existent conditions and design methods of fuzzy adaptive robust controller are given for two classes of external disturbances, respectively. The designed controllers can guarantee the state variables of the closed-loop system to converge, globally, uniformly and exponentially, to a ball in the state space. For the case of nonlinear constraints, the designed controllers can guarantee the state variables of the closed-loop system to converge, globally, uniformly and exponentially, to the equilibrium point by tuning the designed parameters of such controller. The efficiency of our design method is finally verified by simulation on a chaotic system.(4) The main results of the thesis are concluded, and some research issues in future are proposed.