The value function of an asymptotic exit-time optimal control problem

  • M. Motta
  • C. SartoriEmail author


We consider a class of exit-time control problems for nonlinear systems with a nonnegative vanishing Lagrangian. In general, the associated PDE may have multiple solutions, and known regularity and stability properties do not hold. In this paper we obtain such properties and a uniqueness result under some explicit sufficient conditions. We briefly investigate also the infinite horizon problem.

Mathematics Subject Classification (2000)

49J15 93C10 49L20 49L25 93D20 


Optimal control Exit-time problems Viscosity solutions Asymptotic controllability 


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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Dipartimento di MatematicaPaduaItaly

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