Studies On Feedback Control Of Interval Type-2 T-S Fuzzy Systems

Fuzzy control can deal with complicated nonlinear systems, and has been successfully applied to a lot of industrial fields. T-S fuzzy model is a global model formed by a weighted sum of some linear sub-models, and can approximate any smooth nonlinear functions to any specified accuracy within any convex compact sets. In recent years, nonlinear system control based on T-S model has been paid attention and developed greatly. The traditional T-S fuzzy control is often assumed that the fuzzy weight does not include uncertain information, and thus parallel distributed compensator (PDC) scheme is employed to design feedback controllers. Sufficient conditions of existence of the corresponding controllers are derived by Lyapunov stability theory. However, nonlinear systems are often associated with uncertainties in practice, for example, uncertain parameters, immeasurable variables, and/or unknown perturbations. Once conventional T-S fuzzy model is emplyed to represent nonlinear systems subject to parameter uncertainties, the fuzzy weights of T-S fuzzy models may contain uncertain information. As a result, the PDC design technique is inapplicable. In contrast to type-1 fuzzy sets, type-2 fuzzy sets have stronger ability to deal with uncertainties. It is likely to enhance the ability to deal with uncertainties and nonlinearities by generalizing type-2 fuzzy logic to T-S fuzzy models. Interval type-2 T-S fuzzy model is employed to represent nonlinear systems subject to parameter uncertainties in this dissertation. Corresponding interval type-2 fuzzy feedback controllers are designed to stabilize interval type-2 T-S fuzzy systems. Lyapunov stability theory is used to derive sufficient conditions of existence of the corresponding controllers. This dissertation proposes new interval type-2 fuzzy state control methods, and the proposed conditions are less conservative than the existing conditions. Moreover, it is not always possible to measure all state variables in practice. This dissertation deeply studies output feedback control method, and proposes respectively the design algorithms of static output feedback controller, dynamic output feedback controller and observer-based state feedback controller. The work of this dissertation includes the following several aspects:In chapter 2, an interval type-2 fuzzy regional switching controller is proposed to conceive less-conservative stabilization conditions, which is switched by basing on the values of system states. In contrast to single global controller, the proposed controller can enhance the nonlinearity for feedback compensation. The shape information of upper and lower membership functions is considered in design procedure. Less conservative stabilization conditions for guaranteeing the interval type-2 fuzzy closed-loop systems be asymptotically stable are presented in the form of linear matrix inequalities (LMIs).Chapter 3 proposes a new interval type-2 fuzzy state controller for stabilization of interval type-2 T-S fuzzy systems. New membership-function-shape-dependent (MFSD) stabilization conditions in terms of LMIs are derived by employing fuzzy Lyapunov function (FLF). The information about the time derivative of upper and lower membership functions is considered to achieve more relaxed LMI conditions.Chapter 4 is concerned with the stabilization issue of interval type-2 T-S fuzzy systems via static output feedback strategy. By using common quadratic Lyapunov function (CQLF), the membership-function-shape-independent (MFSI) stabilization conditions are derived in the form of LMIs. By utilizing the shape information of upper and lower membership functions, the MFSD stabilization conditions are developed to reduce the conservativeness in design procedure. LMI-based stabilization conditions for interval type-2 fuzzy static output feedback H∞ control synthesis are also derived.Chapter 5 focuses on designing H∞ controllers of interval type-2 T-S fuzzy systems via dynamic output feedback strategy. The interval type-2 fuzzy closed-loop systems are represented as open-loop descriptor system form for obtaining stability conditions in terms of LMIs. The MFSI stabilization conditions for guaranteeing the interval type-2 fuzzy closed-loop systems be asymptotically stable and satisfying H∞ performance are derived by Lyapunov stability theory. The boundary information of cross products of the upper and lower membership functions is employed to introduce several slack matrices in the design procedure and to obtain more relaxed LMI conditions.Chapter 6 focuses on studying observer-based H∞ controller synthesis for interval type-2 T-S fuzzy systems. An interval type-2 fuzzy closed-loop system is formed by an interval type-2 T-S fuzzy model, an interval type-2 fuzzy observer and an observer-based interval type-2 fuzzy controller connected in a closed loop. The MFSI stabilization conditions for guaranteeing the interval type-2 fuzzy closed-loop systems be asymptotically stable and satisfying H∞ performance are derived by Lyapunov stability theory and some matrix inequality techniques. By dividing premise variable domain and considering the local boundary information of upper and lower membership functions in each subdomain, more relaxed MFSD stabilization conditions are obtained.