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What procedure to choose while designing a fuzzy control? towards mathematical foundations of fuzzy control
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Lea, Robert Kreinovich, Vladik YA Quintana Sr., Chris |
| Copyright Year | 1991 |
| Description | Fuzzy control has been successfully applied in industrial systems. However, there is some caution in using it. The reason is that it is based on quite reasonable ideas, but each of these ideas can be implemented in several different ways, and depending on which of the implementations chosen different results are achieved. Some implementations lead to a high quality control, some of them not. And since there are no theoretical methods for choosing the implementation, the basic way to choose it now is experimental. But if one chooses a method that is good for several examples, there is no guarantee that it will work fine in all of them. Hence the caution. A theoretical basis for choosing the fuzzy control procedures is provided. In order to choose a procedure that transforms a fuzzy knowledge into a control, one needs, first, to choose a membership function for each of the fuzzy terms that the experts use, second, to choose operations of uncertainty values that corresponds to 'and' and 'or', and third, when a membership function for control is obtained, one must defuzzy it, that is, somehow generate a value of the control u that will be actually used. A general approach that will help to make all these choices is described: namely, it is proved that under reasonable assumptions membership functions should be linear or fractionally linear, defuzzification must be described by a centroid rule and describe all possible 'and' and 'or' operations. Thus, a theoretical explanation of the existing semi-heuristic choices is given and the basis for the further research on optimal fuzzy control is formulated. |
| File Size | 883765 |
| Page Count | 8 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19930016270 |
| Archival Resource Key | ark:/13960/t9g49m959 |
| Language | English |
| Publisher Date | 1991-01-01 |
| Access Restriction | Open |
| Subject Keyword | Cybernetics Fuzzy Sets Control Systems Design Optimal Control Quality Control Group Theory Centroids Expert Systems Formalism Transformations Mathematics Fuzzy Systems Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Technical Report |
