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Fuzzy associative matrix
About: Fuzzy associative matrix is a research topic. Over the lifetime, 8027 publications have been published within this topic receiving 194790 citations.
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TL;DR: A concise and representative review of the most successful applications of type-2 fuzzy logic in these fields is presented and most of the applications in this review use interval type- 2 fuzzy logic, which is easier to handle and less computational expensive than generalized type-1 fuzzy logic.
229 citations
TL;DR: In this paper, some sufficient conditions for convergence under “max(min)” products of the powers of a square fuzzy matrix and of a fuzzy state process are established.
229 citations
TL;DR: It is proved that this general class of SISO TS fuzzy systems that use any type of continuous input fuzzy sets, TS fuzzy rules with linear consequent and a generalized defuzzifier containing the widely used centroid defuzzifiers as a special case can uniformly approximate any polynomial arbitrarily well.
Abstract: Takagi-Sugeno (TS) fuzzy systems have been employed as fuzzy controllers and fuzzy models in successfully solving difficult control and modeling problems in practice. Virtually all the TS fuzzy systems use linear rule consequent. At present, there exist no results (qualitative or quantitative) to answer the fundamentally important question that is especially critical to TS fuzzy systems as fuzzy controllers and models, "Are TS fuzzy systems with linear rule consequent universal approximators?" If the answer is yes, then how can they be constructed to achieve prespecified approximation accuracy and what are the sufficient renditions on systems configuration? In this paper, we provide answers to these questions for a general class of single-input single-output (SISO) fuzzy systems that use any type of continuous input fuzzy sets, TS fuzzy rules with linear consequent and a generalized defuzzifier containing the widely used centroid defuzzifier as a special case. We first constructively prove that this general class of SISO TS fuzzy systems can uniformly approximate any polynomial arbitrarily well and then prove, by utilizing the Weierstrass approximation theorem, that the general TS fuzzy systems can uniformly approximate any continuous function with arbitrarily high precision. Furthermore, we have derived a formula as part of sufficient conditions for the fuzzy approximation that can compute the minimal upper bound on the number of input fuzzy sets and rules needed for any given continuous function and prespecified approximation error bound, An illustrative numerical example is provided.
227 citations
Book•
01 Dec 1996TL;DR: This chapter discusses the design and implementation of Fuzzy Control Systems' Stability Classes, and discusses the Controllability and Observability of Large-Scale Systems, which are based on the Hierarchical Control method.
Abstract: Preface. 1. Introduction to Large-Scale Systems. Historical Background. Hierarchical Structures. Decentralized Control. Artificial Intelligence. Neural Networks. Fuzzy Logic. Computer-Aided Approach. Scope. Problems. 2. Large-Scale Systems Modeling. Introduction. Aggregation Methods. General Aggregation. Modal Aggregation. Balanced Aggregation. Perturbation Methods. Weakly Coupled Models. Strongly Coupled Models. Modeling via System Identification. Problem Definition. System ID Toolbox. Modeling via Fuzzy Logic. Problems. 3. Structural Properties of Large Scale Systems. Introduction. Lyapunov Stability Methods. Definitions and Problem Statement. Stability Criteria. Connective Stability. Input-Output Stability Methods. Problem Development and Statement. IO Stability Criterion. Controllability and Observability of Composite Systems via Connectivity Approach. Preliminary Definitions. Controllability and Observability Conditions. Structural Controllability and Observability. Structure and Rank of a Matrix. Conditions for Structural Controllability. Structural Controllability and Observability via System Connectability. Computer-Aided Structural Analysis. Standard State-Space Forms. CAD Examples. Discussion and Conclusions. Discussion of the Stability of Large-Scale Systems. Discussion of the Controllability and Observability of Large-Scale Systems. Problems. 4. Hierarchical Control of Large-Scale Systems. Introduction. Coordination of Hierarchical Structures. Model Coordination Method. Goal Coordination Method. Hierarchical Control of Linear Systems. Linear System Two-level Coordination. Interaction Prediction Method. Goal Coordination and Singularities. Closed-Loop Hierarchical Control of Continuous-Time Systems. Series Expansion Approach of Hierarchical Control. Problem Formulation. Performance Index Approximation. Optimal Control. Coorinator Problem. Computer-Aided Hierarchical Control Design Examples. Problems. 5. Decentralized Control of Large-Scale Systems. Introduction. Decentralized Stabilization. Fixed Polynomials and Fixed Modes. Stabilization via Dynamic Compensation. Stabilization via Multilevel Control. Exponential Stabilization. Decentralized Adaptive Control. Decentralized Adaptation. Decentralized Regulation Systems. Decentralized Tracking Systems. Liquid-Metal Cooled Reactor. Application of Model Reference Adaptive Control. Discussion and Conclusions. Problems. 6. Near-Optimum Design of Large-Scale Systems. Introduction. Near-Optimum Control of Linear Time-Invariant Systems. Aggregation Methods. Perturbation Methods. Decentralized Control via Unconstrained Minimization. Near-Optimum Control of Large-Scale Nonlinear Systems. Near-Optimum Control via Sensitivity Methods. Hierarchical Control via Interaction Prediction. Bounds on Near-Optimum Cost Functional. Near-Optimality Due to Aggregation. Near-Optimality Due to Perturbation. Near-Optimality in Hierarchical Control. Near-Optimality in Nonlinear Systems. Computer-Aided Design. Problems. 7. Fuzzy Control Systems-Structures and Stability. Introduction. Fuzzy Control Structures. Basic Definitions and Architectures. Fuzzification. Inference Engine. Defuzzification Methods. The Inverted Pendulum Problem. Overshoot-Suppressing Fuzzy Controllers. Analysis of Fuzzy Control System. Stability of Fuzzy Control Systems. Introduction. Fuzzy Control Systems' Stability Classes. Lyapunov Stability of Fuzzy Control Systems. Fuzzy System Stability via Interval Matrix. Method. Problems. 8. Fuzzy Control Systems-Adaptation and Hierarchy. Introduction. Adaptive Fuzzy Control Systems. Adaptation by Parameter Estimation. Adaptive Fuzzy Multiterm Controllers. Indirect Adaptive Fuzzy Control. Large-Scale Fuzzy Control Systems. Hierarchical Fuzzy Control. Rule-Base Reduction. Hybrid Control Systems. Problems. Appendix A. Brief Review of Fuzzy Set Theory. Introduction. Fuzzy Sets versus Crisp Sets. The Shape of Fuzzy Sets. Fuzzy Sets Operations. Fuzzy Logic and Approximate Reasoning. Problems. Apprendix B. The Fuzzy Logic Development Kit. Introduction. Description of the FULDEK Program. EDITOR Option. The RUN Option. Post-Processing Feature of FULDEK. A Real-Time Laser Beam Fuzzy Controller. New Options in Version 4.0 of the FULDEK Program. Conclusion. References. Index.
227 citations
TL;DR: It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are bounded, and the input and output constraints are circumvented simultaneously.
227 citations