Performance Analysis And Sliding Mode Controller Design Of Interval Type-2 Fuzzy Systems

The interval type-2 fuzzy model has advantages in dealing with the uncertainties of the membership function and reducing computational complexity,marking it one of the powerful tools to deal with nonlinear systems.Sliding mode control has good robustness to system internal parameter perturbation and external interference,and is also widely used in industrial production.For interval type-2 fuzzy systems,the thesis research the finite-time boundedness of the systems and the design problems of adaptive sliding mode controllers.The main contributions of this dissertation are summarized as follows:The first part studies the sliding mode control of interval type-2 fuzzy systems.According to the reaching conditions of sliding mode control,the equivalent controller of the closed-loop systems in the sliding phase of sliding mode motion is obtained;By introducing a partitioning strategy and inequality scaling methods,sufficient criteria for the finite-time boundedness are derived for the systems in the reaching phase and the sliding motion phase of the sliding mode motion;Design a sliding mode controller to guarantee the state of the closed-loop systems can be driven to the integral sliding mode surface within a limited time under the action of the sliding mode controller.Through numerical example simulation verifies the feasibility of the design method.The second part focuses on the sliding mode control problem of interval type-2 fuzzy systems subject to the unmeasurable state and injection attacks.The state observer is constructed to estimate the unmeasurable state,the integral sliding mode surface is constructed based on the estimated value of the state observer,according to the reaching conditions of sliding mode control,the equivalent controller of the closed-loop systems in the sliding phase of sliding mode motion is obtained,so as to obtain the sufficient conditions for the stability of the sliding motion phase;By estimating the unknown parameters in the upper bounds of injection attacks and external disturbances,an adaptive sliding mode controller is synthesized such that the reachability of the specified sliding surface can be guaranteed;Use cone compensation linearization algorithm to transform the nonlinear matrix inequality into a quadratic optimization problem with linear matrix inequality constraints.Numerical example illustrates the effectiveness of the method proposed in this chapter.The third part investigates the problem of adaptive sliding mode control for a class of interval type-2 It(?) stochastic fuzzy systems.The integral sliding function dependent on the upper membership functions is constructed,according to the reaching conditions of the sliding mode control,the equivalent controller of the closed-loop systems in the sliding phase of sliding mode motion is obtained,derive the sufficient conditions for the stability of the closed-loop systems under the action of the equivalent controller;An adaptive scheme is proposed to estimate the unknown parameter related to the systems,and a sliding mode controller based on estimating scheme is designed,such that the reachability of the specified sliding mode surface can be guaranteed;The obtained sufficient condition is a nonlinear matrix inequality,use cone compensation linearization algorithm to transform the nonlinear matrix inequality into a quadratic optimization problem with linear matrix inequality constraints.Numerical example proves the feasibility of the method.