Recursive/Iterative Structure of Multiple Input Fuzzy Controllers

Recursive/Iterative Structure of Multiple Input Fuzzy Controllers with
Unequally Spaced Triangular Membership Functions
MOHAMMAD ROHMANUDDIN1, HOUW-LIONG THE2, ADANG S. AHMAD3,
YUL Y. NAZARUDDIN4
1) Department of Engineering Physics, Institut Teknologi Bandung, Bandung, INDONESIA
2) Department of Physics, Institut Teknologi Bandung, Bandung, INDONESIA
3) Department of Electrical Engineering, Institut Teknologi Bandung, Bandung, INDONESIA
4) Department of Engineering Physics, Institut Teknologi Bandung, Bandung, INDONESIA
Abstract: - In conventional rule based fuzzy control systems, the rules have the form of "IF THEN ." The number of rules increases exponentially as the number of system variables, upon which the fuzzy rules are based, is increased. Some papers showed that, by structuring the rules in a hierarchical way, the total numbers of rules was a linear function of the system variables. In this paper, it is shown that multiple input fuzzy controller of certain class can be represented by recursive/iterative structure of single input fuzzy controllers, upon which each input is applied. As another major result, if there are m input variables, with each universe of discourse divided into (2n+1) fuzzy sets, then the total number of parameters to be determined can be reduced to (m+n). The use of shrinking-span membership functions reduced the total number of parameters to (m+2).

Key-Words: - fuzzy controller, single input, multiple input, multi-layer, unequally spaced membership functions, shrinking-span membership functions, recursive structure, iterative structure.