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Full-Text Articles in Engineering
Sum Normal Optimization Of Fuzzy Membership Functions, Daniel J. Simon
Sum Normal Optimization Of Fuzzy Membership Functions, Daniel J. Simon
Electrical and Computer Engineering Faculty Publications
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 …
Kalman Filtering With State Equality Constraints, Daniel J. Simon, Tien Li Chia
Kalman Filtering With State Equality Constraints, Daniel J. Simon, Tien Li Chia
Electrical and Computer Engineering Faculty Publications
Kalman filters are commonly used to estimate the states of a dynamic system. However, in the application of Kalman filters there is often known model or signal information that is either ignored or dealt with heuristically. For instance, constraints on state values (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. A rigorous analytic method of incorporating state equality constraints in the Kalman filter is developed. The constraints may be time varying. At each time step the unconstrained Kalman filter solution is projected onto the state …