Hung-Yuan Chung

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.

A fuzzy PID controller being like parameter varying PID

A fuzzy-PID controller using the minimum inference engine and center average defuzzification is analyzed and shown that it behaves approximately like a parameter varying PID controller. We then try to analyze the effect of this kind of controller when using different rule bases. Simulation results are used to demonstrate the feasibility of this method.

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.

Upper bound covariance control of discrete perturbed systems

Abstract The purpose of this paper is to develop a methodology, which is based on the state covariance assignment theory, to design feedback controllers such that a specified state covariance upper bound will be achieved. Furthermore, an example is given to illustrate the effectiveness of the present approach.

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

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.

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

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

Abstract Research on covariance control problems for stochastic systems has received rather extensive attention in recent years. In this paper, we focus our attention on the problem of constrained variance design using the covariance control with observed‐state feedback for bilinear stochastic continuous systems. We will modify a practical state covariance assignment theory incorporating the concept of state estimation, and will discuss covariance control for bilinear stochastic continuous systems.