1. Institute of Intelligent Power Electronics – IPE Page1 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. Institute of Intelligent Power Electronics – IPE Page2 Outline Introduction Basic Fuzzy Systems Conventional Dynamical Fuzzy Systems Fuzzy Systems with Linguistic Information Feedback Simulation Results Conclusions and Remarks

3. Institute of Intelligent Power Electronics – IPE Page3 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. Institute of Intelligent Power Electronics – IPE Page4 Basic Fuzzy Systems Feedforward Stucture (Mamdani Type) IF x is A AND (OR) y is B THEN z is C

5. Institute of Intelligent Power Electronics – IPE Page5 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. Institute of Intelligent Power Electronics – IPE Page6 Globally Feedback Fuzzy Systems Output and Crisp Feedback

7. Institute of Intelligent Power Electronics – IPE Page7 Locally Feedback Fuzzy Systems [Lee2000] Internal Memory Units Fuzzy Input Membership Functions Crisp Output

8. Institute of Intelligent Power Electronics – IPE Page8 Crisp Information Feedback Defuzzification: Fuzzy->Nonfuzzy Conversion Unavoidable Information Lost

9. Institute of Intelligent Power Electronics – IPE Page9 Dynamical Fuzzy System with Linguistic Information Feedback Inference Output (Membership Function) is fed back Mamdani Type

10. Institute of Intelligent Power Electronics – IPE Page10 Feedback Parameters

11. Institute of Intelligent Power Electronics – IPE Page11 Diagram of Fuzzy Information Feedback Scheme Linguistic Information Feedback Feedback is controlled by

12. Institute of Intelligent Power Electronics – IPE Page12 Linguistic Information Feedback for Individual Fuzzy Rules

13. Institute of Intelligent Power Electronics – IPE Page13 High-Order Linguistic Information Feedback

14. Institute of Intelligent Power Electronics – IPE Page14 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. Institute of Intelligent Power Electronics – IPE Page15 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. Institute of Intelligent Power Electronics – IPE Page16 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. Institute of Intelligent Power Electronics – IPE Page17 Input and Output Fuzzy Membership Functions

18. Institute of Intelligent Power Electronics – IPE Page18 Step Responses with First-Order Fuzzy Feedback Solid line: max-min composition. Dotted line: sum-product composition

19. Institute of Intelligent Power Electronics – IPE Page19 Step Response with Second-Order Fuzzy Feedback

20. Institute of Intelligent Power Electronics – IPE Page20 Time Sequence Prediction I

21. Institute of Intelligent Power Electronics – IPE Page21 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. Institute of Intelligent Power Electronics – IPE Page22 Input Membership Functions of Fuzzy Predictor

23. Institute of Intelligent Power Electronics – IPE Page23 Evolution of GA-Based Feedback Parameters Optimization

24. Institute of Intelligent Power Electronics – IPE Page24 Prediction Outputs of Fuzzy Predictors Dotted line: static fuzzy predictor. Solid line: dynamical fuzzy predictor

25. Institute of Intelligent Power Electronics – IPE Page25 Time Sequence Prediction II

26. Institute of Intelligent Power Electronics – IPE Page26 Output Membership Functions of Fuzzy Predictor

27. Institute of Intelligent Power Electronics – IPE Page27 Prediction Outputs of Fuzzy Predictors Dotted line: static fuzzy predictor. Solid line: dynamical fuzzy predictor

28. Institute of Intelligent Power Electronics – IPE Page28 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