Evolving Dynamical Systems with the Genetic Algorithm

We use the Genetic Algorithm (GA), a heuristic search and optimization technique inspired by biological evolution, to search for or \evolve" models of partially known nonlinear dynamical systems. We use certain assumptions about the class of \goal" systems (those being modeled), to build constraints into our \model" systems, which consist of functions represented by tables of numbers. Further knowledge is incorporated into our error metric, which is de ned (only) for autonomous dynamical systems. Because we assume that both model and goal systems are autonomous (invariant with respect to translation in time), it is possible to compare them on the basis of the geometry of their respective phase portraits. Thus we formulate a measure, based on phase portrait geometry, of the error or \distance" between dynamical systems. By minimizing the distance separating the model from the goal system, the Genetic Algorithm is usually able to nd an approximation of the goal system. We have used GAdget, our object-oriented implementation of the GA, to evolve models of a variety of linear and non-linear dynamical systems. In particular, we have successfully used the Genetic Algorithm to discover a model of a system described by Van der Pol's equation.

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