Lyapunov-based stability analysis automated by genetic programming

This contribution describes an automatic technique for detecting maximal domains of attraction for nonlinear systems using genetic programming (GP). The theoretical basis for the work is Lyapunov's Direct Method, which provides sufficient conditions for the existence of a region of attraction of a stable focus. In work presented here, our GP approach for defining Lyapunov functions that accurately predict the maximum region of attraction has been extended by defining a target function accounting for level sets. We demonstrate the approach on the analysis of two dynamic systems: (a) van der Pol's equation, which features both a stable and unstable limit cycle; and (b) a model of an exothermic, continuous stirred tank reactor (CSTR), whose stable trajectories tend to move away from the origin before converging.