| Summary: | 碩士 === 國立海洋大學 === 機械與輪機工程學系 === 91 === A complete approach, which is called covariance control theory, for assigning the entire state covariance matrix to the closed-loop systems via state feedback or output feedback controllers has been developed in past years. However, the systems considered in these literatures are often linear ones. Hence, we will attempt to extend the covariance control theory to nonlinear stochastic systems in this thesis. This thesis discusses a class of discrete nonlinear stochastic systems, which are modeled by the Takagi-Sugeno (T-S) fuzzy systems. Because of the dynamics of T-S fuzzy model and nonlinear system are similar; we can represent the nonlinear systems by T-S fuzzy models. According to Parallel Distributed Compensation (PDC) concept, the nonlinear stochastic systems can be driven by the linear feedback gains. In other words, a linear feedback controller can be designed for each local linear model by linear feedback control techniques. The closed-loop fuzzy controller consists of these linear controllers.
In this thesis, we attempt to combine the characteristics of covariance control theory and T-S fuzzy models to deal with the control design problems of the discrete nonlinear stochastic systems. The first half part in the present approach is to assign a common state covariance matrix instead of the common positive definite matrix for the stability conditions of T-S fuzzy systems. In subject to this specified common state covariance matrix, the linear state or output feedback control gains will then be directly solved by the theory of generalized inverse. In the latter half part of this thesis, we derive a method to solve the linear feedback gains for the discrete T-S fuzzy controllers, which can achieve system performance constraints simultaneously. Moreover, the presented control design problem can be reduced to Linear Matrix Inequalities (LMI) problems. Besides, some numerical examples are provided to verify the effects of the proposed method.
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