A note on optimality conditions for optimal exit time problems

Luong V. Nguyen

doi:10.3934/mcrf.2015.5.291

Article Contents

2015, Volume 5, Issue 2: 291-303. Doi: 10.3934/mcrf.2015.5.291

This issue Previous Article Largest space for the stabilizability of the linearized compressible Navier-Stokes system in one dimension Next Article Stability and controllability of a wave equation with dynamical boundary control

A note on optimality conditions for optimal exit time problems

Luong V. Nguyen^1,

1.
Università di Padova, Dipartimento di Matematica, via Trieste 63, 35121 Padova

Received: February 28, 2014

Revised: June 30, 2014

Published: May 2015

Abstract Related Papers Cited by

Abstract

In this note, we obtain some optimality conditions for optimal control problems with exit time similar to those obtained in [Cannarsa, Pignotti and Sinestrari, Discrete Contin. Dynam. Systems 6 (2000), 975 - 997] without requiring an assumption on the Hamiltonian.

Keywords:

Mathematics Subject Classification: Primary: 49K15, 93C15; Secondary: 49J52.

Citation:

Related Papers

Cited by

References

[1]	M. Bardi and I. Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamiltonian-Jacobi-Bellman Equations, Systems & Control: Foundations & Applications, Birkhäuser, Boston, 1997.doi: 10.1007/978-0-8176-4755-1.
[2]	P. Cannarsa, A. Marigonda and K. T. Nguyen, Optimality conditions and regularity results for time optimal control problems with differential inclusions, J. Math. Anal. Appl., 427 (2015), 202-228.doi: 10.1016/j.jmaa.2015.02.027.
[3]	P. Cannarsa, C. Pignotti and C. Sinestrari, Semiconcavity for optimal control problems with exit time, Discrete Contin. Dynam. Systems, 6 (2000), 975-997.doi: 10.3934/dcds.2000.6.975.
[4]	P. Cannarsa and C. Sinestrari, Convexity properties of the minimun time function, Calc. Var. Partial Differential Equations, 3 (1995), 273-298.doi: 10.1007/BF01189393.
[5]	P. Cannarsa and C. Sinestrari, On a class of nonlinear time optimal control problems, Discrete Contin. Dynam. Systems, 1 (1995), 285-300.doi: 10.3934/dcds.1995.1.285.
[6]	P. Cannarsa and C. Sinestrari, Semiconcave Functions, Hamilton-Jacobi Equations and Optimal Control, Progress in Nonlinear Differential Equations and their Applications, 58, Birkhäuser Boston, Inc., Boston, 2004.
[7]	H. Frankowska and L. V. Nguyen, Local regularity of the minimum time function, J. Optim. Theory. Appl., 164 (2005), 68-91.doi: 10.1007/s10957-014-0575-x.
[8]	E. B. Lee and L. Markus, Foundations of Optimal Control Theory, John Wiley & Sons, Inc., New York-London-Sydney, 1967.
[9]	C. Pignotti, Rectifiability results for singular and conjugate points of optimal exit time problems, J. Math. Anal. Appl., 270 (2002), 681-708.doi: 10.1016/S0022-247X(02)00110-5.