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Published in:
2015 | OriginalPaper | Chapter
Discovering Forward Invariant Sets for Nonlinear Dynamical Systems
Authors : James Kapinski, Jyotirmoy Deshmukh
Published in: Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science
Publisher: Springer International Publishing
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Abstract
We describe a numerical technique for discovering forward invariant sets for discrete-time nonlinear dynamical systems. Given a region of interest in the state- space, our technique uses simulation traces originating at states within this region to construct candidate Lyapunov functions, which are in turn used to obtain candidate forward invariant sets. To vet a candidate invariant set, our technique samples a finite number of states from the set and tests them. We derive sufficient conditions on the sample density that formally guarantee that the candidate invariant set is indeed forward invariant. Finally, we present a numerical example illustrating the efficacy of the technique.