The viability kernel algorithm for computing value functions of infinite horizon optimal control problems
type: Item
instance of: scholarly article
title: The viability kernel algorithm for computing value functions of infinite horizon optimal control problems
zbMATH Open document ID: 0862.65039
author: Jean-Pierre Aubin
author: Hélène Frankowska
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-05-25T00:00:00Z
full work available at URL: WP-95-098.pdf
review text: The discounted infinite horizon control problem is considered, which can be characterized using the dynamics \((U,f)\), with the feedbacks \[ x'(t)= f(x(t),u(t)),\quad u(t)\in U(x(t)), \] where the state space \(X\) and the control space \(Z\) are finite-dimensional spaces, \(U:X\to Z\) associates with each state \(x\) the set \(U(x)\) of feasible controls (in general state-dependent), and \(f:\text{Graph}(U)\to X\) describes the dynamics of the system. The epigraph of the solution of such a system is characterized as a viability kernel of an auxiliary differential inclusion. The viability kernel algorithm applied to this problem provides to compute the value function of the discretized optimal control problem as the supremum of a nondecreasing sequence of functions iteratively defined. To prove the convergence of the discrete value function, the authors use the fact, that an upper Painlevé-Kuratowski limit of closed viability domains is a viability domain.
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49K45
Mathematics Subject Classification ID: 49K15
Mathematics Subject Classification ID: 49K40
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 93C42
zbMATH DE Number: 930181
zbMATH Keywords: viability kernel algorithm
zbMATH Keywords: value functions
zbMATH Keywords: infinite horizon optimal control problems
zbMATH Keywords: feedbacks
zbMATH Keywords: differential inclusion
zbMATH Keywords: convergence
zbMATH Keywords: Painlevé-Kuratowski limit
zbMATH Keywords: viability domain
reviewed by: Jiří Vaníček
MaRDI profile type: Publication
OpenAlex ID: W2004561989
DOI: 10.1006/JMAA.1996.0273
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description: scientific article; zbMATH DE number 930181