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Searching for Lyapunov Functions using Genetic Programming

Carl Banks
Virginia Polytechnic Institute and State University, Blacksburg, VA 24060


There is currently no generally-applicable way to find Lyapunov functions for stable nonlinear systems in a reasonable amount of time. However, genetic programming is exciting, new possibility. Genetic programming is a variation of genetic algorithms where the objective space is a space of heirarchial tree structures. The tree structures, among other things, can represnt represent almost any mathematical expression. I have implemented a genetic programming algorithm, in Mathematica, which searches for a Lyapunov function of a given system, where the tree structures represent potential Lyapunov functions. The implementation evaluates the ``Lyapunovness'' of the functions by testing the Lyapunov conditions ($V(x) > 0$ and $\dot
V(x)\leq 0$) at many random points. The implementation was successful somewhat in finding Lypunov functions for simple, two-dimensional systems.

Carl Banks 2002-05-17