The Viability Kernel Algorithm for Computing Value Functions of Infinite Horizon Optimal Control Problems

✍ Scribed by Jean-Pierre Aubin; Hélène Frankowska

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 222 KB
• Volume: 201
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1996.0273

✦ Synopsis

We characterize in this paper the epigraph of the value function of a discounted infinite horizon optimal control problem as the viability kernel of an auxiliary differential inclusion. Then the viability kernel algorithm applied to this problem provides the value function of the discretized optimal control problem as the supremum of a nondecreasing sequence of functions iteratively defined. We also use the fact that an upper Painleve᎐Kuratowski limit of closed viability domains ís a viability domain to prove the convergence of the discrete value functions.