Fuzzy control, Meta-heuristics, Particle swarm optimization, Genetic algorithm, Firefly algorithm, Wavelet. 

The control of non-linear dynamical systems is presented as a problem, due to an in- creasing competitiveness in the industry and the limitations of the classical controls for this purpose. In this context, a better performance can be obtained with fuzzy controllers that can deal with system nonlinearities. The fuzzy controllers, however, have a tuning difficulty, requiring a greater technical knowledge and a greater number of parameters to be adjusted, compared to the classic controls. To overcome this drawback is proposed using metaheuristics, Particle Swarm Optimization, Genetic Algorithm and Firefly Algo- rithm for obtaining the tuning of a fuzzy controller. One of the great difficulties of the approach is to be able to code how good a given controller is, so that the metaheuristic employed can optimize it. Therefore, the mutilevel wavelet analysis, already widely used in the literature for other fins, especially in the analysis of signals, sounds and images, was used to quantify how close the response is to the desired one.The wavelet analysis allows the apprehension of information of the behavior and shape of the signal. This information allows a closer approach to the human human way of evaluating the performance of a con- troller, evaluating whether the response signal obtained has behavior and form similar to the desired response. Mutilevel analysis allows, in addition, to analyze a given frequency of a signal, what is desirable in the design and evaluation of controllers. In this work the use of the mutant wavelet analysis as a cost function of metaheuristics for the tuning of controllers will be studied.