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Topics Covered in Lecture #6

Recap of Lecture #6 (Decision making)

Fuzzy Control

• Comparison of FLC with Conventional Controller
1. Assumptions regarding models, sensors, and processors
2. Proportional Integral Controllers (PI) and Sliding mode vs Fuzzy PIs
3. Common denominator: control surface, deterministic mapping, undistinguishability of design methodology, memory in state vector definition
4. Design Parameters: Gain vectors vs. scaling factors, termsets, and rule sets;
5. Relationship between gains and ratios of scaling factors


• A Knowledge-Based Software View of FLCs
1. A higher level language for the synthesis of Non-Linear Controllers
2. Software Engineering cascade: Development, Compilation, Run-time Phase


• FLC Development Phase
  1. Interpreter: Knowledge Representation, Inference, Control of Inference
     1. Knowledge Representation:
        • Fuzzy Knowledge Base: scaling factors, termsets, rules
        • Input Representation (Quantization or Fuzzification)
        • Fuzzy Control of Type I, II, and III
     2. Inference: Fuzzy mapping and Generalized Modus Ponens
        • Left Hand Side evaluation of fuzzy rules
        • Possibility Measure and Intersection operators
        • Rule firing or detachment (Modus Ponens)
        • Aggregation of rule outputs
     3. Control of inference
        • Defuzzification Methods (Aggregate-and-defuzzify vs Defuzzify-and-Aggregate)
          • Aggregate-and-defuzzify: Mean of Maxima (MOM), Center of Gravity (COG)
          • Defuzzify-and-Aggregate: Height Method (HM), others
        • Tradeoff between performance and cost
  2. Examples
  
  
• FLC Compilation Phase
  1. Exact Methods:
     • Software Architecture and Hardware realizations
     • Coordinate Generation
     • Partitions and Pointers
     • Rules, State Termsets, Output Termset Representation
     • Run-time Engine (Crisp input and Fuzzy input)
  2. Approximate Methods (with no run-time evaluation)
     • Software Architecture and Hardware realizations

  PDF Files of Slides for Lectures 5-6

  PostScript File with Notes on Soft Computing (69 pages - save and send to printer)

  pdf File with Notes on Soft Computing (69 pages: Blank Fig. 6 pg 16, Fig. 18, pg. 37, Fig. 19, pg 38)

  pdf File with the three missing figures ( Fig. 6 pg 16, Fig. 18, pg. 37, Fig. 19, pg 38)

Author: Piero P. Bonissone bonissone@crd.ge.com