Fuzzy Sets and Expert Systems:
Lecture #7 Content
Topics Covered in Lecture #6
Recap of Lecture #6 (Decision making)
Fuzzy Control
- Comparison of FLC with Conventional Controller
- Assumptions regarding models, sensors, and processors
- Proportional Integral Controllers (PI) and Sliding mode vs Fuzzy PIs
- Common denominator: control surface, deterministic mapping,
undistinguishability of design methodology, memory in state vector definition
- Design Parameters: Gain vectors vs. scaling factors, termsets, and rule sets;
- Relationship between gains and ratios of scaling factors
- A Knowledge-Based Software View of FLCs
- A higher level language for the synthesis of Non-Linear Controllers
- Software Engineering cascade: Development, Compilation, Run-time Phase
- FLC Development Phase
- Interpreter: Knowledge Representation, Inference, Control of Inference
- Knowledge Representation:
- Fuzzy Knowledge Base: scaling factors, termsets, rules
- Input Representation (Quantization or Fuzzification)
- Fuzzy Control of Type I, II, and III
- 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
- 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
- Examples
- FLC Compilation Phase
- 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)
- 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)