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A note on optimality conditions for optimal exit time problems
| 1. | Università di Padova, Dipartimento di Matematica, via Trieste 63, 35121 Padova, Italy |
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. |
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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. |
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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. |
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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. |
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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. |
show all references
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. |
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