Intelligent Tuning of Fuzzy Controllers by Learning and Optimization - Fuzzy Modeling and Control: Theory and Applications - page 138

Fig. 7.5 Diagram of the procedure for learning TNFIS based on ECM and backpropagation
7.4 Optimization Techniques for Optimal Setting
of Fuzzy Controllers
The construction of the control rules and the initial membership functions of fuzzy
control systems are relatively easy to set up using a wide range of techniques cur-
rently available such as above described. However, a crucial issue is the setting of
fuzzy control parameters (i.e. scaling factors or scaling gains) which is not a trivial
operation. The tuning of a fuzzy controller aims at achieving a suitable closed-loop
response which accords with certain design specifications; specifications which are
usually dictated by the required system performance (Fig. 7.5 ).
In many situations there are important requirements of the closed-loop dynamic
behaviour (e.g., accuracy and reduction of overshoot, settling time and oscillation)
that cannot be fulfilled without optimal setting of the fuzzy control parameters. A
suitable strategy can be based on the gain margin, the phase margin and an integral
error criterion, but many times this method is limited for processes with low order
dynamics such as first order plus dead-time dynamics. Likewise, the parameters of
the fuzzy controller can also be adjusted by taking a well-tuned linear counterpart
and using some analogies between the scaling factors of the fuzzy controller and the
gains of its linear equivalent.
Optimal tuning of fuzzy controllers on the basis of stochastic and gradient based
optimization strategies has been one of themost active research areas. However, many
of these approaches are limited to simulation studies because of the high complexity
of the optimization algorithms, the need for adequate cost functions or performance
indices and the lack of empirical formulae for practitioners (Haber et al. 2010 ).
Nowadays there is a huge body of literature on deterministic and stochastic meth-
ods for optimal fuzzy control design and self-tuning fuzzy control system design by
applying optimization problems. The analysis and comparison among all available
gradient free optimization methods for optimal tuning of fuzzy control systems is
out the scope of this chapter.
The cross-entropy method was first introduced to estimate the probabilities of
events with very small probabilities. Later it was adapted for optimising systems on