Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Viabilitree: A kd-tree Framework for Viability-based Decision

Abstract : The mathematical viability theory offers concepts and methods that are suitable to study the compatibility between a dynamical system described by a set of differential equations and constraints in the state space. The result sets built during the viability analysis can give very useful information regarding management issues in fields where it is easier to discuss constraints than objective functions. However, computational problems arise very quickly with the number of state variables, and the practical implementation of the method is difficult, although there exists a convergent numerical scheme and several approaches to bypass the computational problems. In order to popularize the use of viability analysis we propose a framework in which the viability sets are represented and approximated with particular kd-trees. The computation of the viability kernel is seen as an active learning problem. We prove the convergence of the algorithm and assess the approximation it produces for known problems with analytical solution. This framework aims at simplifying the declaration of the viability problem and provides useful methods to assist further use of viability sets produced by the computation.
Complete list of metadatas

Cited literature [38 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01319738
Contributor : Isabelle Alvarez <>
Submitted on : Sunday, May 22, 2016 - 10:31:42 PM
Last modification on : Monday, May 18, 2020 - 2:37:21 PM
Document(s) archivé(s) le : Tuesday, August 23, 2016 - 10:17:14 AM

Files

FrameworkForViabilityKBShal.pd...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01319738, version 1

Citation

Isabelle Alvarez, Romain Reuillon, Ricardo de Aldama. Viabilitree: A kd-tree Framework for Viability-based Decision. 2016. ⟨hal-01319738⟩

Share

Metrics

Record views

585

Files downloads

237