Control Design For Interval Type-2 T-S Fuzzy Systems

This dissertation mainly studies the three problems of controller design for interval type-2(IT2)nonlinear systems based on T-S model.Imperfect premise matching of feedback control problems is discussed.The underlying nonlinear systems contain the stochastic perturbations and parameter uncertainties.The primary results in this paper include the following three parts.The first part is concerned with the problem of controller design for IT2 It ?o uncertain stochastic fuzzy systems with a wiener process.Since stochastic perturbations are involved in the underlying systems,the stabilization problem becomes more complex and challenging than that for deterministic systems.Firstly,we construct a IT2 It ?o stochastic fuzzy system,and recall some related stability theory for a class of nonlinear systems with stochastic perturbations.By employing a stochastic Lyapunov approach and a matrix decomposition technique which is effective in dealing with linear fractional uncertainties which involve a multidimensional Wiener process,sufficiency conditions for stabilization of the IT2 stochastic fuzzy systems are established.Finally,a simulation example is given to demonstrate the effectiveness of the proposed method.In the second part,we mainly considers the problem of controller design for IT2 fuzzy systems with parametric uncertainties under imperfect premise matching.The uncertain information exists not only in the membership functions but also in the system itself.The space decomposition method is adopted,dividing state space and footprint of uncertainty(FOU)into some subspaces respectively.Facilitating by space decomposition,the unmatched fuzzy basis functions can be handled in stability analysis.Using the lower and upper membership functions(LUMFs)of each subspace as well as introducing some slack matrix variables,a state feedback controller is developed such that the resulting closed loop system is asymptotically stable.Finally,a simulation example is given to illustrate the effectiveness of the proposed method.In the third part,the problem of state feedback control for IT2 uncertain It ?o stochastic fuzzy systems with a multidimensional Wiener process and unmatched premises is concerned.The uncertainties are of linear fractional form,and appear not only in the membership functions but also in the parametric matrices of the systems.The fuzzy basis functions of the controllers to be designed are different from those of the IT2 fuzzy model.Since stochastic perturbations and unmatched premises as well as parametric uncertainties are involved in the underlying systems,the stabilization problem becomes more complicated and challenging than that for deterministic systems.Facilitating by space decomposition,the LUMFs can be locally represented in terms of the convex combinations of some local basis functions whose coefficients can be obtained via evaluating them at the boundaries of the subspaces decomposed.So the unmatched fuzzy basis functions can be handled in stability analysis of the resulting closed-loop systems with support of these local representations.Then by employing a matrix decomposition technique which is effective in dealing with linear fractional uncertainties which involve a multidimensional Wiener process,a state feedback controller is developed such that the resulting closedloop IT2 system is stochastically asymptotically stable.Finally,a simulation example is given to demonstrate the effectiveness of the proposed method.