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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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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
Outline
  • Introduction
  • Basic Fuzzy Systems
  • Conventional Dynamical Fuzzy Systems
  • Fuzzy Systems with Linguistic Information Feedback
  • Simulation Results
  • Conclusions and Remarks
introduction
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.
basic fuzzy systems
Basic Fuzzy Systems

Feedforward Stucture (Mamdani Type)

IF x is A AND (OR) y is B THEN z is C

conventional dynamical fuzzy systems
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
globally feedback fuzzy systems
Globally Feedback Fuzzy Systems

Output and Crisp Feedback

locally feedback fuzzy systems
Locally Feedback Fuzzy Systems

Internal Memory Units

[Lee2000]

Fuzzy Input Membership Functions

Crisp Output

crisp information feedback
Crisp Information Feedback

Defuzzification: Fuzzy->Nonfuzzy Conversion

Unavoidable Information Lost

dynamical fuzzy system with linguistic information feedback
Dynamical Fuzzy System with Linguistic Information Feedback

Inference Output (Membership Function) is fed back

Mamdani Type

diagram of fuzzy information feedback scheme
Diagram of Fuzzy Information Feedback Scheme

Feedback is controlled by

Linguistic Information Feedback

learning algorithms of feedback parameters
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

advantages of linguistic information feedback
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
simulations
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 ( )
step responses with first order fuzzy feedback
Step Responses with First-Order Fuzzy Feedback

Solid line: max-min composition. Dotted line: sum-product composition

fuzzy predictor with linguistic information feedback
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

prediction outputs of fuzzy predictors
Prediction Outputs of Fuzzy Predictors

Dotted line: static fuzzy predictor.

Solid line: dynamical fuzzy predictor

prediction outputs of fuzzy predictors1
Prediction Outputs of Fuzzy Predictors

Dotted line: static fuzzy predictor.

Solid line: dynamical fuzzy predictor

conclusions
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