Sum Normal Optimization of Fuzzy Membership Functions

Given a fuzzy logic system, how can we determine the membership functions that will result in the best performance? If we constrain the membership functions to a certain shape (e.g., triangles or trapezoids) then each membership function can be parameterized by a small number of variables and the membership optimization problem can be reduced to a parameter optimization problem. This is the approach that is typically taken, but it results in membership functions that are not (in general) sum normal. That is, the resulting membership function values do not add up to one at each point in the domain. This optimization approach is modified in this paper so that the resulting membership functions are sum normal. Sum normality is desirable not only for its intuitive appeal but also for computational reasons in the real time implementation of fuzzy logic systems. The sum normal constraint is applied in this paper to both gradient descent optimization and Kalman filter optimization of fuzzy membership functions. The methods are illustrated on a fuzzy automotive cruise controller

Design and construction of a SMA controlled artificial face.

Thomas Kin Fong Lei.Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.Includes bibliographical references (leaves 64-66).Abstracts in English and Chinese.LIST OF FIGURES --- p.IVChapter 1 --- Introduction --- p.1Chapter 2 --- Model-based Control of SMA Wires --- p.3Chapter 2.1 --- Model Identification of SMA Wires --- p.3Chapter 2.1.1 --- Temperature-Current Relationship --- p.3Chapter 2.1.2 --- Stress-Strain Relationship --- p.5Chapter 2.1.3 --- Martensite Fraction-Temperature Relationship --- p.8Chapter 2.2 --- Model-based Position Control of Two Linking SMA Wires --- p.9Chapter 2.3 --- Summary --- p.12Chapter 3 --- Neural-fuzzy-based Control of SMA Wires --- p.13Chapter 3.1 --- Adaptive Neuro-fuzzy Inference System (ANFIS) --- p.13Chapter 3.1.1 --- ANFIS Architecture --- p.13Chapter 3.1.2 --- Hybrid Learning Algorithm --- p.16Chapter 3.2 --- Generalized Neural Network (GNN) --- p.20Chapter 3.2.1 --- GNN Architecture --- p.20Chapter 3.2.2 --- Approximation of the GNN --- p.22Chapter 3.2.3 --- Backpropagation Training Algorithm --- p.24Chapter 3.2.4 --- Complexity Reduction of the GNN --- p.25Chapter 3.2.5 --- Error Bound of In-exact Reduction of the GNN --- p.29Chapter 3.3 --- Neural-fuzzy-based Position Control of Four Linking SMA Wires --- p.32Chapter 3.3.1 --- ANFIS-based Position Control of Four Linking SMA Wires --- p.32Chapter 3.3.2 --- GNN-based Position Control of Four Linking SMA Wires --- p.35Chapter 3.3.3 --- Performance Comparison of ANFIS and GNN Algorithms --- p.37Chapter 3.4 --- Summary --- p.39Chapter 4 --- SMA Actuated Artificial Face --- p.40Chapter 4.1 --- Muscles of the Human Face --- p.40Chapter 4.2 --- The Software Part: facial model --- p.41Chapter 4.3 --- The Hardware Part: artificial face and peripheral interface --- p.43Chapter 4.3.1 --- SMA Actuated Artificial Face --- p.43Chapter 4.3.2 --- Peripheral Interface --- p.45Chapter 4.4 --- Position Control on the Artificial Face --- p.47Chapter 4.4.1 --- Model-based Position Control on Artificial Face --- p.48Chapter 4.4.2 --- Neural-fuzzy-based Position Control on Artificial Face --- p.49Chapter 4.4.3 --- Comparison of the Model-based and Reduced GNN Control of Artificial Face --- p.49Chapter 4.5 --- Experimental Result --- p.50Chapter 5 --- Conclusion --- p.52Appendix1 --- p.53Appendix2 --- p.55Appendix3 --- p.56Appendix4 --- p.58Bibliography --- p.6