From the Publisher:
A comprehensive treatment of model-based fuzzy control systems
This volume offers full coverage of the systematic framework for the stability and design of nonlinear fuzzy control systems. Building on the Takagi-Sugeno fuzzy model, authors Tanaka and Wang address a number of important issues in fuzzy control systems, including stability analysis, systematic design procedures, incorporation of performance specifications, numerical implementations, and practical applications.
Issues that have not been fully treated in existing texts, such as stability analysis, systematic design, and performance analysis, are crucial to the validity and applicability of fuzzy control methodology. Fuzzy Control Systems Design and Analysis addresses these issues in the framework of parallel distributed compensation, a controller structure devised in accordance with the fuzzy model.
This balanced treatment features an overview of fuzzy control, modeling, and stability analysis, as well as a section on the use of linear matrix inequalities (LMI) as an approach to fuzzy design and control. It also covers advanced topics in model-based fuzzy control systems, including modeling and control of chaotic systems. Later sections offer practical examples in the form of detailed theoretical and experimental studies of fuzzy control in robotic systems and a discussion of future directions in the field.
Fuzzy Control Systems Design and Analysis offers an advanced treatment of fuzzy control that makes a useful reference for researchers and a reliable text for advanced graduate students in the field.

Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach

Fuzzy logic control was originally introduced and developed as a model free control design approach. However, it unfortunately suffers from criticism of lacking of systematic stability analysis and controller design though it has a great success in industry applications. In the past ten years or so, prevailing research efforts on fuzzy logic control have been devoted to model-based fuzzy control systems that guarantee not only stability but also performance of closed-loop fuzzy control systems. This paper presents a survey on recent developments (or state of the art) of analysis and design of model based fuzzy control systems. Attention will be focused on stability analysis and controller design based on the so-called Takagi-Sugeno fuzzy models or fuzzy dynamic models. Perspectives of model based fuzzy control in future are also discussed

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A Survey on Analysis and Design of Model-Based Fuzzy Control Systems

A direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control, is capable of incorporating fuzzy if-then control rules directly into the controllers, and guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded is developed. The specific formula for the bounds is provided, so that controller designers can determine the bounds based on their requirements. The direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the Duffing chaotic system to track a trajectory. The simulation results show that the controller worked without using any fuzzy control rules, and that after fuzzy control rules were incorporated the adaptation speed became much faster. It is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control. >

Stable adaptive fuzzy control of nonlinear systems

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 Sugeno's 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 Sugeno's 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.

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"

The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...

Fuzzy sets and systems

A new approach to the stability analysis of fuzzy linguistic control (FLC) systems is presented. Specifically, it is shown that the direct method of Lyapunov can be used to determine sufficient conditions for global stability of a broad class of fuzzy control schemes. Moreover, a measure of robustness is proposed that can be used to evaluate and possibly redesign a given fuzzy control system so as to enhance the range of its stable operation. Finally, the application of the proposed methodology is shown and its implications in terms of control design are demonstrated by means of numeric examples. >

Stability of fuzzy linguistic control systems

Presents a self organizing fuzzy linguistic control strategy that is based on on-line modification of the control rules according to the extent of deviation of the process output from the output of a given reference model. Accordingly, the learning/adaptation algorithm, which is based on the hill climbing approach, modifies the parametrized characteristic functions of the fuzzy subsets describing the control rules, such that the meaning of each rule is iteratively changed to reflect new information regarding the behavior of the process. Simulation results show that this technique improves the overall response of the system in presence of asymmetric dynamic characteristics of the process, proving that this strategy can be a suitable alternative to ordinary fuzzy control. In order to study this self organizing scheme, the authors used a simulation model with similar characteristics as the gas metal arc welding process. This model simulates the variation of the peak surface temperature of the workpiece directly underneath the weld bead in response to changes in the arc current, or more accurately, changes in the electrode wire feedrate. >

Self organizing fuzzy linguistic control with application to arc welding

In this paper, it is shown that the optimal damping ratio for linear second-order systems that results in minimum-time no-overshoot response to step inputs is of bang-bang type. The optimal damping ratio is zero at the outset and is switched to some maximum value at an appropriate instant of time. The switching time is shown to be a function of the maximum damping ratio and the system natural frequency. Furthermore, it is shown that the larger the maximum damping ratio is, the shorter it takes for the system to reach the desired set point. Finally, it is shown that, if the optimal damping ratio is switched as a function of the system state, then the minimum-time no-overshoot criterion is satisfied, irrespective of the magnitude of the uncertainty in the value of the system natural frequency.

Optimal damping ratio for linear second-order systems

It is shown that the optimal damping ratio for linear second-order systems that results in minimum-time no-overshoot response to step inputs is of the bang-bang type: the optimal damping ratio is zero at the outset and is switched to some maximum value at an appropriate instant of time. The switching time is shown to be a function of the maximum damping ratio and system natural frequency. Furthermore, it is shown that the larger the maximum damping ratio is, the less time it takes for the system to reach the desired set point. Finally, it is shown that, if the optimal damping ratio is switched as a function of the system state, then the minimum-time no-overshoot criterion is satisfied, irrespective of the magnitude of uncertainty in the value of the system natural frequency. >

G. Langari

Papers

Stability of fuzzy linguistic control systems

Self organizing fuzzy linguistic control with application to arc welding

Optimal damping ratio for linear second-order systems

Optimal damping ratio for linear second-order systems