Computing the Viability Kernel Using Level Sets

Sigifredo Laengle () and Tomás Laengle-Aliaga ()
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Sigifredo Laengle: University of Chile
Tomás Laengle-Aliaga: University of Chile

A chapter in Operations Research Proceedings 2024, 2025, pp 135-140 from Springer

Abstract: Abstract The most relevant challenge of the viability kernel computation is efficiently representing sets of states. The classical Saint-Pierre algorithm shows an accelerated explosion of states even in reduced dimensions, attributed to its grid-based representation. On the other hand, in the context of the reachability problem, representations based on constrained polynomials zonotopes and on a discretization of space-time dimensions have been proposed. While the latter does not solve the problem generated by the high dimension, the former raises questions about error propagation. Therefore, we propose investigating the representation level sets whose operations use convolution operators. According to our research, this line of study has not yet been proposed for calculating viable sets. To move in this direction, we compute the viability kernel in level set representation of a linear problem with non-convex state sets. This representation allows us to transform the kernel computation into a sequence of optimisation problems. Moreover, although this initial study does not guarantee efficiency and effectiveness, it offers the theoretical underpinning of convex analysis and clear parallel processing options. Thus, our proposal allows us to initiate an attractive research agenda for computing the viability kernel of high-dimensional problems.

Keywords: viability theory; computing viability kernel; constrained polynomial zonotopes; level sets (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnopch:978-3-031-92575-7_19

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DOI: 10.1007/978-3-031-92575-7_19

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