Robust fuzzy control subject to state variance and passivity constraints for perturbed nonlinear systems with multiplicative noises.

The multi-constrained robust fuzzy control problem is investigated in this paper for perturbed continuous-time nonlinear stochastic systems. The nonlinear system considered in this paper is represented by a Takagi-Sugeno fuzzy model with perturbations and state multiplicative noises. The multiple performance constraints considered in this paper include stability, passivity and individual state variance constraints. The Lyapunov stability theory is employed to derive sufficient conditions to achieve the above performance constraints. By solving these sufficient conditions, the contribution of this paper is to develop a parallel distributed compensation based robust fuzzy control approach to satisfy multiple performance constraints for perturbed nonlinear systems with multiplicative noises. At last, a numerical example for the control of perturbed inverted pendulum system is provided to illustrate the applicability and effectiveness of the proposed multi-constrained robust fuzzy control method.

H(∞) constrained fuzzy control via state observer feedback for discrete-time Takagi-Sugeno fuzzy systems with multiplicative noises.

The purpose of this paper is to study the H(∞) constrained fuzzy controller design problem for discrete-time Takagi-Sugeno (T-S) fuzzy systems with multiplicative noises by using the state observer feedback technique. The proposed fuzzy controller design approach is developed based on the Parallel Distributed Compensation (PDC) technique. Through the Lyapunov stability criterion, the stability analysis is completed to develop stability conditions for the closed-loop systems. Besides, the H(∞) performance constraints is also considered in the stability condition derivations for the worst case effect of disturbance on system states. Solving these stability conditions via the two-step Linear Matrix Inequality (LMI) algorithm, the observer-based fuzzy controller is obtained to achieve the stability and H(∞) performance constraints, simultaneously. Finally, a numerical example is provided to verify the applicability and effectiveness of the proposed fuzzy control approach.

Fuzzy controller design for passive continuous-time affine T-S fuzzy models with relaxed stability conditions.

In order to design a fuzzy controller for complex nonlinear systems, the work of this paper deals with developing the relaxed stability conditions for continuous-time affine Takagi-Sugeno (T-S) fuzzy models. By applying the passivity theory and Lyapunov theory, the relaxed stability conditions are derived to guarantee the stability and passivity property of closed-loop systems. Based on these relaxed stability conditions, the synthesis of fuzzy controller design problem for passive continuous-time affine T-S fuzzy models can be easily solved via the Optimal Convex Programming Algorithm (OCPA) and Linear Matrix Inequality (LMI) technique. At last, a simulation example for the fuzzy control of a nonlinear synchronous generator system is presented to manifest the applications and effectiveness of proposed fuzzy controller design approach.

T-S region-based fuzzy control with multiple performance constraints.

Takagi-Sugeno fuzzy control problems with minimizing H2/Hinfinity norm are investigated in this paper. A redesigned T-S fuzzy model and controller are called a T-S Region-based Fuzzy Model (TSRFM) and a T-S Region-based Fuzzy Controller (TSRFC), respectively, which are derived from the fuzzy region concept and the robust control technique. The fuzzy region concept is used to divide the general plant rules into several fuzzy regions and the robust control technique is used to stabilize all plant rules of each fuzzy region. In this case, the stability conditions with H2/Hinfinity performance are derived from Lyapunov criterion, which are expressed in terms of LMIs. For the fuzzy model involving large plant rules, the proposed idea greatly reduces the total number of LMIs and controller rules so that TSRFC is easy to implement with simple hardware. Although the controller rules are reduced, TSRFC is able to provide performance as good as former designs.

Synthesis of nonlinear discrete control systems via time-delay affine Takagi-Sugeno fuzzy models.

The affine Takagi-Sugeno (TS) fuzzy model played a more important role in nonlinear control because it can be used to approximate the nonlinear systems more than the homogeneous TS fuzzy models. Besides, it is known that the time delays exist in physical systems and the previous works did not consider the time delay effects in the analysis of affine TS fuzzy models. Hence a parallel distributed compensation based fuzzy controller design issue for discrete time-delay affine TS fuzzy models is considered in this paper. The time-delay effect is considered in the discrete affine TS fuzzy models and the stabilization issue is developed for the nonlinear time-delay systems. Finally, a numerical simulation for a time-delayed nonlinear truck-trailer system is given to show the applications of the present approach.

Robust covariance control for discrete system by Takagi-Sugeno fuzzy controllers.

Variances of the system states or outputs often play vital roles in the problem for performance requirements of many stochastic control systems. For linear stochastic systems, the covariance control technique has been applied to deal with the variance constrained design problem. This paper extends this technique to a class of discrete-time nonlinear perturbed stochastic systems, which are modeled by the Takagi-Sugeno (TS) fuzzy systems. By fuzzy IF-THEN rules, which represent local linear input-output relations, the nonlinear systems can be described by TS fuzzy models. According to the parallel distributed compensation (PDC) concept, the discrete-time nonlinear perturbed stochastic systems can be driven by the linear feedback gains. The purpose of this paper is to provide a method to design an output feedback fuzzy controller, which is based on the upper bound state covariance control technique and PDC concept, for the discrete-time perturbed stochastic systems using TS fuzzy models.

Covariance control with observed-state feedback gains for continuous nonlinear systems using T-S fuzzy models.

The design problem of state variance constrained control for stochastic systems has received rather extensive attention in recent years. This paper solves the state variance constrained controller design problem by using the covariance control theory, with observed-state feedback gains for continuous Takagi-Sugeno (TS) fuzzy models. By incorporating the technique of state estimation into the practical covariance control theory, a variance constrained control methodology is developed for the continuous TS fuzzy models. Finally, a numerical example is shown to demonstrate the efficiency and applicability of the proposed approach.