Calculation Formula of the Viability Kernel in Convex and Linear Dynamical Systems

Sigifredo Laengle () and Tomás Laengle-Aliaga ()
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Sigifredo Laengle: Faculty of Economics and Business, University of Chile
Tomás Laengle-Aliaga: Faculty of Physical and Mathematical Sciences, University of Chile

Chapter Chapter 79 in Operations Research Proceedings 2023, 2025, pp 617-623 from Springer

Abstract: Abstract The most critical problem of viability theory is determining the initial states of a dynamical system for which at least one solution remains in the same set. This problem is analogous to many real situations, particularly management problems modelled as high-dimensional dynamic systems. However, the high dimensionality hampers the practical utility of the theory. The existing literature reports difficulties with models of more than four dimensions. Therefore, we investigate the current algorithms and study a calculation formula for high-dimensional linear and convex problems. We found a formula for viable sets in case of backward invariance of the environment set. Finally, since many dynamical systems are neither convex nor linear, extending our work to such systems is the immediate challenge.

Keywords: Viability theory; Viability kernel; Computing viability kernel (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/978-3-031-58405-3_79

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