Intelligent Tuning of Fuzzy Controllers by Learning and Optimization - Fuzzy Modeling and Control: Theory and Applications - page 139

Fig. 7.6 Conceptual scheme for optimal setting of fuzzy control based on optimization techniques

the assumption that sampling around the optimum of a function has a very small
probability.
For the optimization of fuzzy control parameters (for example, K e , K ce ) based on

a suitable criterion, the closed-loop system is considered to be a stochastic system.
Therefore, the cross-entropy method is applied as a population based optimization
algorithm in such a way that it uses the scores of the trial runs as optimal in a rhetorical
sense. In the next section the main rationale of the cross entropy method is addressed
as well as the main design steps. For the sake of clarity in this chapter only this
method for optimal tuning is considered.

7.4.1 Cross Entropy for Optimal Tuning
of Fuzzy Controllers

The cross-entropy method was first introduced to estimate the probabilities of events
with very small probabilities. Later it was adapted for optimizing systems on the
assumption that sampling around the optimum of a function has a very small proba-
bility. The main difference between the optimal tuning by learning and the optimal
setting by optimization is that this strategy uses a population based optimization
method for fuzzy control systems on the basis of simulation. The overall control
scheme is shown in Fig. 7.6 . Therefore, the three key elements are:

• a rough model of the plant,

• a performance index or performance indices, and

• the initial fuzzy controller and the optimization method.

In the optimization of fuzzy control parameters such as the scaling factors or gain

( on the basis of a suitable criterion, the closed-loop system is considered to

be a stochastic system. Therefore, the cross-entropymethod is applied as a population
based optimization algorithm in the sense that it utilizes the scores of the trial runs
as optimal in a rhetorical sense.

K e , K ce )