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## Computación y Sistemas

*Print version* ISSN 1405-5546

#### Abstract

FLORES-ANDO, Fortunato; AGUILAR-IBANEZ, Carlos; SUAREZ-CASTANON, Miguel S and CUEVAS DE LA ROSA, Francisco. **An Identification Genetic Algorithm for a Family of Duffing's System**.* Comp. y Sist.* [online]. 2003, vol.7, n.2, pp.102-112.
ISSN 1405-5546.

This paper shows a simple way to recover the whole unknown parameters set of the Duffing's oscillator by using a genetic algorithm. The fact that the system is observable and constructible with respect to a suitable output helps in obtaining an integral parameterization of the output. Subsequently an integral parameterization of the output which depends upon the unknown parameters, and, a random estimation of the output is proposed, assuming that the set of unknown parameters are contained into a bounded set. This random estimation is chosen provided that the error between the actual output and the estimated output minimizes the errors of a quadratic function. The minimization problem and the random estimations of the output are formulated directly in terms of a genetic algorithm. A population of chromosomes is codified with the parameters of the Duffing's oscillator system. A fitness function is established to evaluate the chromosomes, in such a way that it minimizes the errors of a quadratic function. The chromosomes' population evolves till a fitness average threshold is obtained. This method is numerically possible and easy to implement in a digital computer.

**Keywords
:
**Mechanical Oscillator; Chaos; Genetic Algorithms; Reconstruction.