Skip to main content
×
Home
    • Aa
    • Aa

On asymptotic exit-time control problems lacking coercivity

  • M. Motta (a1) and C. Sartori (a1)
Abstract

The research on a class of asymptotic exit-time problems with a vanishing Lagrangian, begun in [M. Motta and C. Sartori, Nonlinear Differ. Equ. Appl. Springer (2014).] for the compact control case, is extended here to the case of unbounded controls and data, including both coercive and non-coercive problems. We give sufficient conditions to have a well-posed notion of generalized control problem and obtain regularity, characterization and approximation results for the value function of the problem.

The research on a class of asymptotic exit-time problems with a vanishing Lagrangian, begun in [M. Motta and C. Sartori, Nonlinear Differ. Equ. Appl. Springer (2014).] for the compact control case, is extended here to the case of unbounded controls and data, including both coercive and non-coercive problems. We give sufficient conditions to have a well-posed notion of generalized control problem and obtain regularity, characterization and approximation results for the value function of the problem.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

P. Cannarsa and G. Da Prato , Nonlinear optimal control with infinite horizon for distributed parameter systems and stationary Hamilton–Jacobi equations. SIAM J. Control and Optim. 27 (1989) 861875.

P. Cannarsa and C. Sinestrari , Convexity properties of the minimum time function. J. Calc. Var. Partial Differ. Eqs. 3 (1995) 273298.

F. Da Lio , On the Bellman equation for infinite horizon problems with unbounded cost functional. J. Appl. Math. Optim. 41 (2000) 171197.

M. Garavello and P. Soravia , Optimality principles and uniqueness for Bellman equations of unbounded control problems with discontinuous running cost. Nonlinear Differ. Equ. Appl. 11 (2004) 271298.

M. Malisoff , Bounded-from-below solutions of the Hamilton–Jacobi equation for optimal control problems with exit times: vanishing Lagrangians, eikonal equations, and shape-from-shading. Nonlinear Differ. Equ. Appl. 11 (2004) 95122.

M. Motta and F. Rampazzo , Asymptotic controllability and optimal control. J. Differ. Eqs. 254 (2013) 27442763.

F. Rampazzo and C. Sartori , Hamilton-Jacobi-Bellman equations with fast gradient-dependence. Indiana Univ. Math. J. 49 (2000) 10431077.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

ESAIM: Control, Optimisation and Calculus of Variations
  • ISSN: 1292-8119
  • EISSN: 1262-3377
  • URL: /core/journals/esaim-control-optimisation-and-calculus-of-variations
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 4 *
Loading metrics...

Abstract views

Total abstract views: 25 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 19th September 2017. This data will be updated every 24 hours.