Construction of Lyapunov functions on the domain of asymptotic nullcontrollability : Numerics

Titelangaben

Camilli, Fabio ; Grüne, Lars ; Wirth, Fabian:
Construction of Lyapunov functions on the domain of asymptotic nullcontrollability : Numerics.
In: IFAC Proceedings Volumes. Bd. 37 (2004) Heft 13 . - S. 715-720.
ISSN 1474-6670
DOI: https://doi.org/10.1016/S1474-6670(17)31309-5

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Abstract

We present a numerical method for the computation of control Lyapunov functions on the domain of nullcontrollability of a nonlinear system. We apply an adaptive semi--Lagrangian discretization technique to a generalized version of the Zubov equation whose solutions provide such Lyapunov functions. In particular, we address regularization issues which need to be resolved before the scheme is applicable and discuss an adaptive space discretization technique.