Asymptotic problems in optimal control  with a vanishing Lagrangian and  unbounded data

Monica Motta; Caterina Sartori

doi:10.3934/dcds.2015.35.4527

Article Contents

2015, Volume 35, Issue 9: 4527-4552. Doi: 10.3934/dcds.2015.35.4527

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Asymptotic problems in optimal control with a vanishing Lagrangian and unbounded data

Monica Motta^1, and
Caterina Sartori^2,

1.
Dipartimento di Matematica Pura ed Applicata, Via Trieste, 63, 35121 Padova
2.
Dipartimento di Matematica, Via Trieste, 63, 35121 Padova

Received: March 31, 2014

Revised: August 31, 2014

Published: May 2017

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Abstract

In this paper we give a representation formula for the limit of the finite horizon problem as the horizon becomes infinite, with a nonnegative Lagrangian and unbounded data. It is related to the limit of the discounted infinite horizon problem, as the discount factor goes to zero. We give sufficient conditions to characterize the limit function as unique nonnegative solution of the associated HJB equation. We also briefly discuss the ergodic problem.

Keywords:

Asymptotic behaviour,
optimal control problems with unbounded data,
impulsive controls,
unbounded viscosity solutions.

Mathematics Subject Classification: Primary: 35B40; Secondary: 49J15, 49N25, 49L25.

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