## Optimal strategy of switching reasoning methods in fuzzy control.(English)Zbl 0897.93036

Yager, Ronald R. (ed.) et al., Theoretical aspects of fuzzy control. Proceedings of the 2nd IEEE conference on fuzzy systems, March 1993, San Francisco, CA, USA. New York, NY: Wiley. 117-146 (1995).
There are some approaches to fuzzy control methodology. The main difference between them is how they interpret the logical connectives “or” and “and”, that is, what reasoning method these approaches use. It is shown that varying reasoning methods for different stages of the plant lead to better control results [M. H. Smith, Proc. Second Int. Workshop on Industrial Application of Fuzzy Control and Intelligent Systems, College Station, 118-121 (1992); Proc. Second IEEE-FUZZ Int. Conf., San Francisco, CA, 1, 968-973 (1993); M. H. Smith and H. Takagi, Fifth Int. Fuzzy Systems Association World Congress, Seoul, Korea, 1354-1357 (1993)].
The main goal of the present work is to describe the optimal strategy of switching reasoning methods in fuzzy control of the plant. The main criteria for choosing a set of reasoning methods are 1) a relaxation time, that is, the first moment of time starting from which $$| x(t)| \leq| x(0) |/M$$, where $$x(t)$$ is a trajectory of the plant and $$M$$ is some positive number, and 2) a nonsmoothness $$J(x)= \int^\infty_0 (\dot x(t))^2dt$$. Under these criteria the possible choices among reasoning methods are described. Several results explaining which choice of reasoning methods leads to a better control are proved in the work. These results are explained using the illustration of a simple plant.
All the results have been experimentally confirmed by application of different reasoning methods to the control of an inverted pendulum on a cart. Finally some open problems are stated.
For the entire collection see [Zbl 0834.00063].

### MSC:

 93C42 Fuzzy control/observation systems 93B12 Variable structure systems