# A Dynamic Programming Approach to Viability Problems

* Corresponding author
1 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal, Inria Lille - Nord Europe
Abstract : Viability theory considers the problem of maintaining a system under a set of viability constraints. The main tool for solving viability problems lies in the construction of the viability kernel, defined as the set of initial states from which there exists a trajectory that remains in the set of constraints indefinitely. The theory is very elegant and appears naturally in many applications. Unfortunately, the current numerical approaches suffer from low computational efficiency, which limits the potential range of applications of this domain. In this paper we show that the viability kernel is the zero-level set of a related dynamic programming problem, which opens promising research directions for numerical approximation of the viability kernel using tools from approximate dynamic programming. We illustrate the approach using $k-$nearest neighbors on a toy problem in two dimensions and on a complex dynamical model for anaerobic digestion process in four dimensions.
Document type :
Preprints, Working Papers, ...

Cited literature [13 references]

https://hal.archives-ouvertes.fr/hal-00125248
Contributor : Pierre-Arnaud Coquelin <>
Submitted on : Thursday, January 18, 2007 - 4:11:04 PM
Last modification on : Tuesday, November 24, 2020 - 2:18:20 PM
Long-term archiving on: : Wednesday, April 7, 2010 - 2:19:43 AM

### File

viabilite.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-00125248, version 1

### Citation

Pierre-Arnaud Coquelin, Sophie Martin, Rémi Munos. A Dynamic Programming Approach to Viability Problems. 2007. ⟨hal-00125248⟩

Record views