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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:
93D05Lyapunov and other classical stabilities of control systems
90C59Approximation methods and heuristics
93C15Control systems governed by ODE
93C10Nonlinear control systems
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References:
[1] Grosman, B.; Lewin, D. R.: Adaptive genetic programming for steady-state process modeling, Computers and chemical engineering 28, No. 12, 2779-2790 (2004)
[2] Grosman, B., & Lewin, D. R. (2005). Automatic Generation of Lyapunov Functions using Genetic Programming, 16th IFAC world congress, Prague
[3] Koza, J. R.: Genetic programming: on the programming of computers by means of natural selection, (1992) · Zbl 0850.68161
[4] Lyapunov, A. M.: Problème général de la stabilité du mouvement, Ann. fac. Sci. Toulouse 9, 203-474 (1949)
[5] Slotine, J. J. E.; Li, W.: Applied nonlinear control, (1991) · Zbl 0753.93036
[6] Vannelli, A.; Vidyasagar, M.: Maximal Lyapunov functions and domains of attraction for autonomous nonlinear systems, Automatica 21, No. 1, 69-80 (1985) · Zbl 0559.34052 · doi:10.1016/0005-1098(85)90099-8
[7] Vidyasagar, M.: Nonlinear system analysis, (1993) · Zbl 0900.93132