Intelligent tools for the state space analysis of nonlinear controllers

The author describes research on automating the state space analysis of nonlinear dynamical systems by combining artificial intelligence with numerical software. The resulting programs can assist control theorists in the stability and robustness analysis of continuous and discrete nonlinear systems. A program POINCARE, that analyzes one-parameter systems with two state variables is described. It computes the stable states as a function of the parameter value and describes the basins of attraction qualitatively. It computes basins numerically for fixed parameter values. The algorithm extends to systems where two parameters vary independently. It extends partially to systems with three or more state variables; tracking attractors is feasible, but estimating basins requires more research.<
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