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A Dynamical Fuzzy System with Linguistic Information Feedback

A Dynamical Fuzzy System with Linguistic Information Feedback. Xiao-Zhi Gao and Seppo J. Ovaska Institute of Intelligent Power Electronics Department of Electrical and Communications Engineering Helsinki University of Technology, Finland. Outline. Introduction Basic Fuzzy Systems

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A Dynamical Fuzzy System with Linguistic Information Feedback

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  1. A Dynamical Fuzzy System with Linguistic Information Feedback Xiao-Zhi Gao and Seppo J. Ovaska Institute of Intelligent Power Electronics Department of Electrical and Communications Engineering Helsinki University of Technology, Finland

  2. Outline • Introduction • Basic Fuzzy Systems • Conventional Dynamical Fuzzy Systems • Fuzzy Systems with Linguistic Information Feedback • Simulation Results • Conclusions and Remarks

  3. Introduction • Fuzzy logic theory has found successful applications in industrial engineering • Most fuzzy systems applied in practice are static • static input-output mappings • no internal dynamics • A new dynamical fuzzy model with linguistic information feedback is proposed • suitable for dynamical system modeling, control, filtering, time series prediction, etc.

  4. Basic Fuzzy Systems Feedforward Stucture (Mamdani Type) IF x is A AND (OR) y is B THEN z is C

  5. Conventional Dynamical Fuzzy Systems • Classical fuzzy systems lack necessary internal dynamics • can only realize static mappings • Feedback is needed to introduce dynamics • Two kinds of conventional recurrent fuzzy systems • Globally feedback fuzzy systems • Locally feedback fuzzy systems • Crisp information feedback

  6. Globally Feedback Fuzzy Systems Output and Crisp Feedback

  7. Locally Feedback Fuzzy Systems Internal Memory Units [Lee2000] Fuzzy Input Membership Functions Crisp Output

  8. Crisp Information Feedback Defuzzification: Fuzzy->Nonfuzzy Conversion Unavoidable Information Lost

  9. Dynamical Fuzzy System with Linguistic Information Feedback Inference Output (Membership Function) is fed back Mamdani Type

  10. Feedback Parameters

  11. Diagram of Fuzzy Information Feedback Scheme Feedback is controlled by Linguistic Information Feedback

  12. Linguistic Information Feedback for Individual Fuzzy Rules

  13. High-Order Linguistic Information Feedback

  14. Learning Algorithms of Feedback Parameters • Feedback parameters have a nonlinear relationship with system output • It is difficult to derive an explicit learning algorithm • Some general-purpose algorithms can be applied to optimize feedback parameters • genetic algorithms (GA) nonlinear operators

  15. Advantages of Linguistic Information Feedback • 1. Rich fuzzy inference output is fed back without any information transformation and loss • 2. Local feedback connections can store temporal patterns • Suitable for dynamical system identification • 3. Training of feedback coefficients leads to an equivalent update of output membership functions • Benefit of adaptation

  16. Simulations • A simple dynamical fuzzy system with linguistic information feedback • single-input-single-output • two inference rules • IF X is Small THEN Y is Small • IF X is Large THEN Y is Large • max-min and sum-product composition • COA defuzzification • Step input ( )

  17. Input and Output Fuzzy Membership Functions

  18. Step Responses with First-Order Fuzzy Feedback Solid line: max-min composition. Dotted line: sum-product composition

  19. Step Response with Second-Order Fuzzy Feedback

  20. Time Sequence Prediction I

  21. Fuzzy Predictor with Linguistic Information Feedback • Four fuzzy rules are constructed • IF x(k) is [-1] THEN x(k+1) is [0] • IF x(k) is [0] THEN x(k+1) is [1] • IF x(k) is [1] THEN x(k+1) is [0] • IF x(k) is [0] THEN x(k+1) is [-1] Rule 2 and Rule 4 are conflicting Linguistic information feedback can correct

  22. Input Membership Functions of Fuzzy Predictor

  23. Evolution of GA-Based Feedback ParametersOptimization

  24. Prediction Outputs of Fuzzy Predictors Dotted line: static fuzzy predictor. Solid line: dynamical fuzzy predictor

  25. Time Sequence Prediction II

  26. Output Membership Functions of Fuzzy Predictor

  27. Prediction Outputs of Fuzzy Predictors Dotted line: static fuzzy predictor. Solid line: dynamical fuzzy predictor

  28. Conclusions • A new dynamical fuzzy system with linguistic information feedback is proposed • Dynamical properties of our fuzzy model are shown • Present paper is a starting point for our future work under this topic • more simulations are needed • extension to Sugeno type fuzzy sytems • extension to feedforward structure • extension to premise part • applications in dynamical system identification

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