1 / 23

Neuro-Fuzzy Control

Neuro-Fuzzy Control. Adriano Joaquim de Oliveira Cruz NCE/UFRJ adriano@nce.ufrj.br. Neuro-Fuzzy Systems. Usual neural networks that simulate fuzzy systems Introducing fuzziness into neurons. ANFIS architecture. Adaptive Neuro Fuzzy Inference System

melina
Download Presentation

Neuro-Fuzzy Control

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Neuro-Fuzzy Control Adriano Joaquim de Oliveira Cruz NCE/UFRJ adriano@nce.ufrj.br

  2. Neuro-Fuzzy Systems • Usual neural networks that simulate fuzzy systems • Introducing fuzziness into neurons

  3. ANFIS architecture • Adaptive Neuro Fuzzy Inference System • Neural system that implements a Sugeno Fuzzy model.

  4. Sugeno Fuzzy Model • A typical fuzzy rule in a Sugeno fuzzy model has the form If x is A and y is B then z = f(x,y) • A and B are fuzzy sets in the antecedent. • z=f(x,y)is a crisp function in the consequent. • Usually z is a polynomial in the input variables x and y. • When z is a first-order polynomial the system is called a first-order Sugeno fuzzy model.

  5. Sugeno Fuzzy Model z1=p1x+q1y+r1 m m A1 B1 w1 y x m m B2 A2 w2 y x z2=p2x+q2y+r2

  6. Sugeno First Order Example • If x is small then y = 0.1x + 6.4 • If x is median then y = -0.5x + 4 • If x is large then y = x – 2 Reference: J.-S. R. Jang, C.-T. Sun and E. Mizutani, Neuro-Fuzzy and Soft Computing

  7. Comparing Fuzzy and Crisp

  8. Sugeno Second Order Example • If x is small and y is small then z = -x + y +1 • If x is small and y is large then z = -y + 3 • If x is large and y is small then z = -x + 3 • If x is large and y is large then z = x + y + 2 Reference: J.-S. R. Jang, C.-T. Sun and E. Mizutani, Neuro-Fuzzy and Soft Computing

  9. Membership Functions

  10. Output Surface

  11. Layer 1 Layer 2 Layer 3 Layer 4 Layer 5 x y A1 w1 x O1,2 P N A2 f S B1 P N y w2 B2 x y ANFIS Architecture • Output of the ith node in the l layer is denoted as Ol,i

  12. ANFIS Layer 1 • Layer 1: Node function is • x and y are inputs. • Ai and Bi are labels (e.g. small, large). • m(x) can be any parameterised membership function. • These nodes are adaptive and the parameters are called premise parameters.

  13. ANFIS Layer 2 • Every node output in this layer is defined as: • T is T-norm operator. • In general, any T-norm that perform fuzzy AND can be used, for instance minimum and product. • These are fixed nodes.

  14. ANFIS Layer 3 • The ith node calculates the ratio of the ith rule’s firing strength to the sum of all rules’ firing strength • Outputs of this layer are called normalized firing strengths. • These are fixed nodes.

  15. ANFIS Layer 4 • Every ith node in this layer is an adaptive node with the function • Outputs of this layer are called normalized firing strengths. • pi, qi and ri are the parameter set of this node and they are called consequent parameters.

  16. ANFIS Layer 5 • The single node in this layer calculates the overall output as a summation of all incoming signals.

  17. ANFIS Layer 5 • Every ith node in this layer is an adaptive node with the function • Outputs of this layer are called normalized firing strengths.

  18. Alternative Structures • The structure is not unique. • For instance layers 3 and 4 can be combined or weight normalisation can be performed at the last layer.

  19. S / Alternative Structure cont. Layer 1 Layer 2 Layer 3 Layer 4 Layer 5 x y A1 w1 S x P A2 f O1,2 B1 P y w2 B2 x y

  20. Training Algorithm • The function f can be written as • There is a hybrid learning algorithm based on the least-squares method and gradient descent.

  21. Example • Modeling the function • Input range [-10,+10]x[-10,+10] • 121 training data pairs • 16 rules, with four membership functions assigned to each input. • Fitting parameters = 72; 24 premise and 48 consequent parameters.

  22. Initial and Final MFs

  23. Training Data

More Related