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

In: Operations Research Proceedings 2023

Author

Listed:
  • Sigifredo Laengle

    (Faculty of Economics and Business, University of Chile)

  • Tomás Laengle-Aliaga

    (Faculty of Physical and Mathematical Sciences, University of Chile)

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.

Suggested Citation

  • Sigifredo Laengle & Tomás Laengle-Aliaga, 2025. "Calculation Formula of the Viability Kernel in Convex and Linear Dynamical Systems," Lecture Notes in Operations Research, in: Guido Voigt & Malte Fliedner & Knut Haase & Wolfgang Brüggemann & Kai Hoberg & Joern Meissner (ed.), Operations Research Proceedings 2023, chapter 0, pages 617-623, Springer.
    • Handle: RePEc:spr:lnopch:978-3-031-58405-3_79
    DOI: 10.1007/978-3-031-58405-3_79
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