Machine tuning of stable analytical fuzzy predictive controllers

Authors:
Piotr M. Marusak
Affiliations:
Institute of Control and Computation Engineering, Warsaw University of Technology, Warszawa, Poland
Venue:
ICANNGA'09 Proceedings of the 9th international conference on Adaptive and natural computing algorithms
Year:
2009

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Abstract

Analytical fuzzy predictive controllers are composed of a few local controllers grouped in the fuzzy Takagi-Sugeno model. Usually, they are designed using the PDC method. Stability of the resulting system (controller + control plant) may be checked using variants of Lyapunov stability criterion. One of the first such variants was the criterion developed by Tanaka and Sugeno. It is rather conservative criterion because, in its basic form, it does not take into consideration the shape of the membership functions. However, this drawback can be exploited in the proposed approach. After finding the Lyapunov matrix for the system with the analytical fuzzy predictive controller, using e.g. LMIs, it is possible to change the membership functions of the controller without sacrificing stability. It is done using the heuristic method. Thus, practically any shape of membership functions may be assumed.