Hua O. Wang

Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs

This paper presents new relaxed stability conditions and LMI- (linear matrix inequality) based designs for both continuous and discrete fuzzy control systems. They are applied to design problems of fuzzy regulators and fuzzy observers. First, Takagi and Sugenos fuzzy models and some stability results are recalled. To design fuzzy regulators and fuzzy observers, nonlinear systems are represented by Takagi-Sugenos (TS) fuzzy models. The concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the TS fuzzy models. New stability conditions are obtained by relaxing the stability conditions derived in previous papers, LMI-based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions. Other LMIs with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures. Design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the LMI-based design procedures.

Comments on "Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H/sup /spl infin// control theory, and linear matrix inequalities"

This paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems, First, a stability condition for Takagi and Sugenos fuzzy model is given in terms of Lyapunov stability theory. Next, new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization, H/sup /spl infin// control theory, and linear matrix inequalities. The derived stability conditions are used to analyze the stability of Takagi and Sugenos fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems, The design method employs the so-called parallel distributed compensation, important issues for the stability analysis and design are remarked. Finally, three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented.

A multiple Lyapunov function approach to stabilization of fuzzy control systems

This paper addresses stability analysis and stabilization for Takagi-Sugeno fuzzy systems via a so-called fuzzy Lyapunov function which is a multiple Lyapunov function. The fuzzy Lyapunov function is defined by fuzzily blending quadratic Lyapunov functions. Based on the fuzzy Lyapunov function approach, we give stability conditions for open-loop fuzzy systems and stabilization conditions for closed-loop fuzzy systems. To take full advantage of a fuzzy Lyapunov function, we propose a new parallel distributed compensation (PDC) scheme that feedbacks the time derivatives of premise membership functions. The new PDC contains the ordinary PDC as a special case. A design example illustrates the utility of the fuzzy Lyapunov function approach and the new PDC stabilization method.

A unified approach to controlling chaos via an LMI-based fuzzy control system design

This paper presents a unified approach to controlling chaos via a fuzzy control system design based on linear matrix inequalities (LMIs). First, Takagi-Sugeno fuzzy models and some stability results are recalled. To design fuzzy controllers, chaotic systems are represented by Takagi-Sugeno fuzzy models. The concept of parallel distributed compensation is employed to determine structures of fuzzy controllers from the Takagi-Sugeno fuzzy models, LMI-based design problems are defined and employed to find feedback gains of fuzzy controllers satisfying stability, decay rate, and constraints on control input and output of fuzzy control systems. Stabilization, synchronization, and chaotic model following control for chaotic systems are realized via the unified approach based on LMIs. An exact linearization (EL) technique is presented as a main result in the stabilization. The EL technique also plays an important role in the synchronization and the chaotic model following control. Two cases are considered in the synchronization. One is the feasible case of the EL problem. The other is the infeasible case of the EL problem. Furthermore, the chaotic model following control problem, which is more difficult than the synchronization problem, is discussed using the EL technique. Simulation results show the utility of the unified design approach based on LMIs proposed in this paper.

BIFURCATION CONTROL: THEORIES, METHODS, AND APPLICATIONS

Bifurcation control deals with modification of bifurcation characteristics of a parameterized nonlinear system by a designed control input. Typical bifurcation control objectives include delaying t...

A Descriptor System Approach to Fuzzy Control System Design via Fuzzy Lyapunov Functions

There has been a flurry of research activities in the analysis and design of fuzzy control systems based on linear matrix inequalities (LMIs). This paper presents a descriptor system approach to fuzzy control system design using fuzzy Lyapunov functions. The design conditions are still cast in terms of LMIs but the proposed approach takes advantage of the redundancy of descriptor systems to reduce the number of LMI conditions which leads to less computational requirement. To obtain relaxed LMI conditions, new types of fuzzy controller and fuzzy Lyapunov function are proposed. A salient feature of the LMI conditions derived in this paper is to relate the feasibility of the LMIs to the switching speed of each linear subsystem (to be exact, to the lower bounds of time derivatives of membership functions). To illustrate the validity and applicability of the proposed approach, two design examples are provided. The first example shows that the LMI conditions based on the fuzzy Lyapunov function are less conservative than those based on a common (standard) Lyapunov function. The second example illustrates the utility of the fuzzy Lyapunov function approach in comparison with a piecewise Lyapunov function approach.

Model construction, rule reduction, and robust compensation for generalized form of Takagi-Sugeno fuzzy systems

This paper presents a systematic procedure of fuzzy control system design that consists of fuzzy model construction, rule reduction, and robust compensation for nonlinear systems. The model construction part replaces the nonlinear dynamics of a system with a generalized form of Takagi-Sugeno fuzzy systems, which is newly developed by us. The generalized form has a decomposed structure for each element of A/sub i/ and B/sub i/ matrices in consequent parts. The key feature of this structure is that it is suitable for constructing IF-THEN rules and reducing the number of IF-THEN rules. The rule reduction part provides a successive procedure to reduce the number of IF-THEN rules. Furthermore, we convert the reduction error between reduced fuzzy models and a system to model uncertainties of reduced fuzzy models. The robust compensation part achieves the decay rate controller design guaranteeing robust stability for the model uncertainties. Finally, two examples demonstrate the utility of the systematic procedure developed.

A Sum-of-Squares Approach to Modeling and Control of Nonlinear Dynamical Systems With Polynomial Fuzzy Systems

This paper presents a sum of squares (SOS) approach for modeling and control of nonlinear dynamical systems using polynomial fuzzy systems. The proposed SOS-based framework provides a number of innovations and improvements over the existing linear matrix inequality (LMI)-based approaches to Takagi-Sugeno (T-S) fuzzy modeling and control. First, we propose a polynomial fuzzy modeling and control framework that is more general and effective than the well-known T--S fuzzy modeling and control. Secondly, we obtain stability and stabilizability conditions of the polynomial fuzzy systems based on polynomial Lyapunov functions that contain quadratic Lyapunov functions as a special case. Hence, the stability and stabilizability conditions presented in this paper are more general and relaxed than those of the existing LMI-based approaches to T-S fuzzy modeling and control. Moreover, the derived stability and stabilizability conditions are represented in terms of SOS and can be numerically (partially symbolically) solved via the recently developed SOSTOOLS. To illustrate the validity and applicability of the proposed approach, a number of analysis and design examples are provided. The first example shows that the SOS approach renders more relaxed stability results than those of both the LMI-based approaches and a polynomial system approach. The second example presents an extensive application of the SOS approach in comparison with a piecewise Lyapunov function approach. The last example is a design exercise that demonstrates the viability of the SOS-based approach to synthesizing a stabilizing controller.

Electroencephalogram-based control of an electric wheelchair

This paper presents a study on electroencephalogram (EEG)-based control of an electric wheelchair. The objective is to control the direction of an electric wheelchair using only EEG signals. In other words, this is an attempt to use brain signals to control mechanical devices such as wheelchairs. To achieve this goal, we have developed a recursive training algorithm to generate recognition patterns from EEG signals. Our experimental results demonstrate the utility of the proposed recursive training algorithm and the viability of accomplishing direction control of an electric wheelchair by only EEG signals.

Takagi-sugeno fuzzy-model-based fault detection for networked control systems with Markov delays

A Takagi-Sugeno (T-S) model is employed to represent a networked control system (NCS) with different network-induced delays. Comparing with existing NCS modeling methods, this approach does not require the knowledge of exact values of network-induced delays. Instead, it addresses situations involving all possible network-induced delays. Moreover, this approach also handles data-packet loss. As an application of the T-S-based modeling method, a parity-equation approach and a fuzzy-observer-based approach for fault detection of an NCS were developed. An example of a two-link inverted pendulum is used to illustrate the utility and viability of the proposed approaches