Wen-Jer Chang

Constrained fuzzy controller design of discrete Takagi-Sugeno fuzzy models

The motivation for the work presented in this paper results from the need to find fuzzy controllers with a common observability Gramian for discrete Takagi-Sugeno fuzzy systems. The developed approach is based on the parallel distributed compensation concept. For each rule of the discrete Takagi-Sugeno fuzzy model, the present approach will show a way to parametrize the static linear output feedback control gains for achieving a certain common observability Gramian for all subsystems. A numerical example will be given to illustrate the utility of the proposed technique.

Passive fuzzy controller design for nonlinear systems with multiplicative noises

Abstract This paper proposes a passive fuzzy controller design methodology for nonlinear system with multiplicative noises. Applying the Itos formula and the sense of mean square, the sufficient conditions are developed to analyze the stability and to design the controller for stochastic nonlinear systems which are represented by the Takagi–Sugeno (T–S) fuzzy models. The sufficient conditions derived in this paper belong to the Linear Matrix Inequality (LMI) forms which can be solved by the convex optimal programming algorithm. Besides, the passivity theory is applied to discuss the effect of external disturbance on system. Finally, some numerical simulation examples are provided to demonstrate the applications of the proposed fuzzy controller design technique.

Robust fuzzy control for uncertain stochastic time-delay Takagi--Sugeno fuzzy models for achieving passivity

This paper focuses on the robust passive stability and stabilization problems for uncertain nonlinear stochastic time-delay systems. Via the fuzzy modeling approach, the nonlinear stochastic system is described by Takagi-Sugeno (T-S) fuzzy model in which the consequent parts are presented by linear stochastic time-delay differential equation. With Lyapunov-Krasovskii function and improved Jensens inequality, the stability criteria are derived. In addition, the passivity theory is employed to discuss external disturbance effect on system for achieving attenuation performance. According to the proposed design method, the fuzzy controller is carried out by parallel distributed compensation (PDC) concept to guarantee the robust asymptotical stability and attenuation performance of system in the sense of mean square. Finally, a synchronous generator power system is presented to manifest the application and effectiveness of the proposed fuzzy control method.

Covariance control with variance constraints for continuous perturbed stochastic systems

Abstract This paper proposes an approach which deals with the variance constraints for the perturbed stochastic systems. The purpose of this approach is to develop a novel methodology, which is based on the theory of covariance control, to solve the constrained variance design problem for the linear perturbed stochastic systems. Particular attention is paid to the case in which there are only uncertain perturbations in the state dynamic matrix. Moreover, an example is given to illustrate the power of the technique.

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.

A Covariance Controller Design Incorporating Optimal Estimation for Nonlinear Stochastic Systems

This note addresses the problem of constrained variance design with minimizing LQG cost function via the method of covariance control incorporating the optimal estimation for nonlinear stochastic systems. The nonlinear stochastic systems are first linearized and then are examined by way of the technique of describing functions. Finally, an application of this approach to a position servomechanism is illustrated by a numerical example.

AQM router design for TCP network via input constrained fuzzy control of time-delay affine Takagi–Sugeno fuzzy models

In this article, Takagi–Sugeno (T–S) fuzzy control theory is proposed as a key tool to design an effective active queue management (AQM) router for the transmission control protocol (TCP) networks. The probability control of packet marking in the TCP networks is characterised by an input constrained control problem in this article. By modelling the TCP network into a time-delay affine T–S fuzzy model, an input constrained fuzzy control methodology is developed in this article to serve the AQM router design. The proposed fuzzy control approach, which is developed based on the parallel distributed compensation technique, can provide smaller probability of dropping packets than previous AQM design schemes. Lastly, a numerical simulation is provided to illustrate the usefulness and effectiveness of the proposed design approach.

Analysis and synthesis of discrete nonlinear passive systems via affine T-S fuzzy models

The article considers the analysis and synthesis problem for the discrete nonlinear systems, which are represented by the discrete affine Takagi–Sugeno (T–S) fuzzy models. The state feedback fuzzy controller design methodology is developed to guarantee that the affine T–S fuzzy models achieve Lyapunov stability and strict input passivity. In order to find a suitable fuzzy controller, an Iterative Linear Matrix Inequality (ILMI) algorithm is employed in this article to solve the stability conditions for the closed-loop affine T–S fuzzy models. Finally, the application of the proposed fuzzy controller design methodology is manifested via a numerical example with computer simulations.

PDC and Non-PDC fuzzy control with relaxed stability conditions for contintuous-time multiplicative noised fuzzy systems

Abstract This paper presents a relaxed scheme of fuzzy controller design for continuous-time nonlinear stochastic systems that are constructed by the Takagi–Sugeno (T–S) fuzzy models with multiplicative noises. Through Nonquadratic Lyapunov Functions (NQLF) and Non-Parallel Distributed Compensation (Non-PDC) control law, the less conservative Linear Matrix Inequality (LMI) stabilization conditions on solving fuzzy controllers are derived. Furthermore, in order to study the effects of stochastic behaviors on dynamic systems in real environments, the multiplicative noise term is introduced in the consequent part of fuzzy systems. For decreasing the conservatism of the conventional PDC-based fuzzy control, the NQLF stability synthesis approach is developed in this paper to obtain relaxed stability conditions for T–S fuzzy models with multiplicative noises. Finally, some simulation examples are provided to demonstrate the validity and applicability of the proposed fuzzy controller design 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.