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Lyapunov-based stability analysis automated by genetic programming. (English) Zbl 1154.93405
Summary: This contribution describes an automatic technique to detect suitable Lyapunov functions for nonlinear systems. The theoretical basis for the work is Lyapunov’s Direct Method, which provides sufficient conditions for stability of equilibrium points. In our proposed approach, Genetic Programming (GP) is used to search for suitable Lyapunov functions, that is, those that best predict the true domain of attraction. In the work presented here, our GP approach has been extended by defining a target function accounting for the Lyapunov function level sets.

MSC:
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
90C59 Approximation methods and heuristics in mathematical programming
93C15 Control/observation systems governed by ordinary differential equations
93C10 Nonlinear systems in control theory
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