Chein-Chung Sun

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.

Discrete

The purpose of this paper is to develop a fuzzy controller to stabilize a discrete nonlinear model in which the controller rule is adjustable and it is developed for stabilizing Takagi-Sugeno (T-S) fuzzy models involving lots of plant rules. The design idea is to partition the fuzzy model into several fuzzy regions, and regard each region as a polytopic model. The proposed fuzzy controller is called the T-S fuzzy region controller (TSFRC) where the controller rule has to stabilize all plant rules of the fuzzy region and guarantee the whole fuzzy system is asymptotically stable. The stability analysis is derived from Lyapunov stability criterion in which the robust compensation is considered and is expressed in terms of linear matrix inequalities. Comparing with parallel distributed compensation (PDC) designs, TSFRC is easy to be designed and to be implemented with simple hardware or microcontroller. Even if the controller rules are reduced, TSFRC is able to provide competent performances as well as PDC-based designs

H_{2}/H_{\infty}

This paper is concerned with the synthesis of a mixed H 2 /H∞ robust static output feedback with a bounded control bandwidth for continuous-time uncertainty systems. To this end, genetic algorithms and a linear matrix inequality solver are employed to regulate the static output feedback gains and to examine the Lyapunov stability conditions, respectively. The fitness function of this paper, which is called a hierarchical fitness function structure (HFFS), is able to deal with the stability conditions and the performance constraints in turn. This HFFS not only saves computing time but can also identify the infeasible stability condition. Designers can use the proposed idea to deal with many complex output feedback control problems. It also limits elaborate mathematical derivations and extra constraints.

Nonlinear Controller Design Based on Fuzzy Region Concept and Takagi–Sugeno Fuzzy Framework

Based on the Gramian assignment technique, a continuous fuzzy controller for a class of uncertain nonlinear systems is developed. These nonlinear systems considered are represented by Takagi-Sugeno fuzzy models. The design of this fuzzy controller can be accomplished by assigning a certain common observability Gramian for each rule of these Takagi-Sugeno fuzzy models.

H2∕H∞ Robust Static Output Feedback Control Design via Mixed Genetic Algorithm and Linear Matrix Inequalities

This paper attempts to use fuzzy-region concept and robust control techniques to design Takagi-Sugeno (T-S) fuzzy-region controller (FRC). To this end, the preliminary is to convert general fuzzy models into fuzzy-region ones. The stability conditions for closed-loop fuzzy-region systems are derived from a quadratic Lyapunov function, which are expressed in terms of linear matrix inequalities (LMIs). Therefore, LMl optimization can be employed in solving FRC. From the implementation point of view, FRC is embedded easily in microchip and is able to avoid time consuming in defuzzification. From the design point of view, FRC can greatly reduce the amount of LMIs, and remove the mutual influence of PDC concept. The feasibility and validity of this approach are demonstrated by a numerical example.

Fuzzy control with common observability Gramian assignment for continuous Takagi-Sugeno models

A simple Takagi-Sugeno (TS) fuzzy controller design method is proposed, which is based on the genetic algorithm (GA) and generalized inverse theory. The eigenvalues problems of LMI could be implemented by this approach. The proposed method can automatically seek the feedback gains without complex mathematical derivations. In this paper, we implement the TS fuzzy controller design problems in an alternative way.

Design of Takagi-Sugeno fuzzy-region controller based on fuzzy-region concept, rule reduction and robust control technique

This paper presents a new structure of Takagi-Sugeno (T-S) fuzzy controllers, which is called T-S fuzzy region controller or TSFRC for short. The fuzzy region concept is used to partition the plant rules into several fuzzy regions so that only one region is fired at the instant of each input vector being coming. Because each fuzzy region contains several plant rules, the fuzzy region can be regarded as a polytopic uncertain model. Therefore, robust control techniques would be essential for designing the feedback gains of each fuzzy region. To improve the speed of response, the decay rate constraint is imposed when deriving the stability conditions with Lyapunov stability criterion. To design TSFRC with the linear matrix inequality (LMI) solver, all stability conditions are represented in terms of LMIs. Finally, a two-link robot system is used to prove the feasibility and validity of the proposed method. DOI: 10.1115/1.2431811

Design the T-S fuzzy controller for a class of T-S fuzzy models via genetic algorithm

In this paper, the output feedback controller design problem with robust S-stability constraint is considered. The S-stability constraint denotes that the controller can stabilize the uncertain system and shift all closed-loop poles of nominal system inside a specific conic sector s. We intend to simple genetic algorithm (SGA) to seek these robust output feedback gains. To this end, we develop the hierarchical fitness function structure (HFFS) to combine the stability conditions so that the fitness value corresponds to the stable degree of closed-loop system. These stability conditions of HFFS are derived by means of the concept of family of polynomials, generalized edge theorem and Hurwitz testing matrix. The proposed design algorithm is named the robust S stability output feedback controller design algorithm (RSOFCDA).

Design of Takagi-Sugeno Fuzzy Region Controller Based on Rule Reduction, Robust Control, and Switching Concept

We would like to thank Liu et al. for their interest in our work and for their careful examination of our paper. We agree that our approach can only be valid for a certain type of nonlinear systems, which can be represented by the discrete T–S fuzzy model with the output of the system being a linear function of the states. In the case of output being a nonlinear function of the states, Liu et al. provided a theorem to modify the stability conditions of Lemma 1 of our paper. According to these new stability conditions, the fuzzy controllers of Example 2 of our paper should be redesigned since the output of the system is a nonlinear function of the states. However, the main contribution of our paper is to provide a methodology to design fuzzy controller such that the common observability Gramian can be assigned by the designers. These results are stated in Sections 3 and 4 of our paper, which are not a7ected by the modi8cation of Liu et al. At last, we are thankful to the comments, which give us more insight to our problem.

GA-based robust S-stability output feedback controller design algorithm with hierarchical fitness function structure

For the design problem of active suspension systems, the purpose of compensator is to suppress the road disturbances and to tolerate the different body mass. From the control viewpoints, this kind of compensators is equal to the robust controller for which the H/sub 2/ norm is minimized. In this paper, we attempt to use a Simple Genetic Algorithm (SGA) to find out the compensator. The notion is that all elements of compensator are randomly given. The compensator is determined by use of the fitness function which is composed of stability conditions, i.e., we determine the compensator according to the grade of stability. Thus we derive new stability conditions and convert them into numerals. To enhance the computing speed, we propose a Hierarchical Fitness Function Structure (HFFS) to merge these numerals into a unique fitness value. Based on these quantified stability conditions, HFFS and SGA, we can find the compensator without using complex mathematical derivation. Besides, we derive the new stability conditions by using the concept of family of polynomials, the generalized edge theorem, Hurwitz testing matrix and some simple control concept rather than using Lyapunov stability criteria. The purpose is to relax the stability constraints.