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A general theorem on necessary conditions in optimal control
Lipschitz continuity of optimal control and Lagrange multipliers in a problem with mixed and pure state constraints
| 1. | Faculdade de Engenharia da Universidade do Porto, Department of Electrical Engineering and Computers, Porto, Portugal |
| 2. | Department of Mathematics and Computer Science, Penn State Harrisburg, Middletown, PA 17057, United States |
References:
| [1] |
J. F. Bonnans and A. Hermant, Second-order analysis for optimal control problems with pure state constraints and mixed control-state constraints, Ann. I. H. Poincaré - Analyse Non Linéaire, 26 (2009), 561-598. |
| [2] |
J. F. Bonnans and A. Shapiro, "Perturbation Analysis of Optimization Problems," Springer-Verlag, New York, 2000. |
| [3] |
A. V. Dmitruk, Maximum principle for a general optimal control problem with state and regular mixed constraints, Comp. Math. and Modeling, 4 (1993), 364-377.
doi: doi:10.1007/BF01128760. |
| [4] |
G. N. Galbraith and R. B. Vinter, Lipschitz Continuiuty of Optimal Controls for State Constrained Problems, SIAM J. Control and Optimization, 42 (2003), 1727-1744.
doi: doi:10.1137/S0363012902404711. |
| [5] |
W. W. Hager, Lipschitz continuity for constrained processes, SIAM J. Control and Optimization, 17 (1979), 321-338.
doi: doi:10.1137/0317026. |
| [6] |
K. Malanowski, On the regularity of solutions to optimal control problems for systems linear with respect to control variable, Arch. Auto. i Telemech., 23 (1978), 227-241. |
| [7] |
K. Malanowski, On normality of Lagrange multipliers for state constrained optimal control problems, Optimization, 52 (2003), 75-91.
doi: doi:10.1080/0233193021000058940. |
| [8] |
A. A. Milyutin, A. V. Dmitruk and N. P. Osmolovsky, "Maximum Principle in Optimal Control" (Russian), Moscow State University Press, 2004. Available online at http://www.milyutin.ru/book.html. |
| [9] |
S. M. Robinson and R. H. Day, A sufficient condition for continuity of optimal sets in mathematical programming, J. Math. Anal. Appl., 45 (1974), 506-511.
doi: doi:10.1016/0022-247X(74)90089-4. |
| [10] |
S. M. Robinson, Strongly regular generalized equations, Mathematics of Operations Research, 5 (1980), 43-62.
doi: doi:10.1287/moor.5.1.43. |
| [11] |
I. Shvartsman and R. B. Vinter, Regularity properties of optimal controls for state constrained problems with time-varying control constraints, Nonlinear Analysis: Theory, Methods and Applications, 65 (2006), 448-474. |
| [12] |
R. B. Vinter, "Optimal Control," Birkhäuser, Boston, 2000. |
show all references
References:
| [1] |
J. F. Bonnans and A. Hermant, Second-order analysis for optimal control problems with pure state constraints and mixed control-state constraints, Ann. I. H. Poincaré - Analyse Non Linéaire, 26 (2009), 561-598. |
| [2] |
J. F. Bonnans and A. Shapiro, "Perturbation Analysis of Optimization Problems," Springer-Verlag, New York, 2000. |
| [3] |
A. V. Dmitruk, Maximum principle for a general optimal control problem with state and regular mixed constraints, Comp. Math. and Modeling, 4 (1993), 364-377.
doi: doi:10.1007/BF01128760. |
| [4] |
G. N. Galbraith and R. B. Vinter, Lipschitz Continuiuty of Optimal Controls for State Constrained Problems, SIAM J. Control and Optimization, 42 (2003), 1727-1744.
doi: doi:10.1137/S0363012902404711. |
| [5] |
W. W. Hager, Lipschitz continuity for constrained processes, SIAM J. Control and Optimization, 17 (1979), 321-338.
doi: doi:10.1137/0317026. |
| [6] |
K. Malanowski, On the regularity of solutions to optimal control problems for systems linear with respect to control variable, Arch. Auto. i Telemech., 23 (1978), 227-241. |
| [7] |
K. Malanowski, On normality of Lagrange multipliers for state constrained optimal control problems, Optimization, 52 (2003), 75-91.
doi: doi:10.1080/0233193021000058940. |
| [8] |
A. A. Milyutin, A. V. Dmitruk and N. P. Osmolovsky, "Maximum Principle in Optimal Control" (Russian), Moscow State University Press, 2004. Available online at http://www.milyutin.ru/book.html. |
| [9] |
S. M. Robinson and R. H. Day, A sufficient condition for continuity of optimal sets in mathematical programming, J. Math. Anal. Appl., 45 (1974), 506-511.
doi: doi:10.1016/0022-247X(74)90089-4. |
| [10] |
S. M. Robinson, Strongly regular generalized equations, Mathematics of Operations Research, 5 (1980), 43-62.
doi: doi:10.1287/moor.5.1.43. |
| [11] |
I. Shvartsman and R. B. Vinter, Regularity properties of optimal controls for state constrained problems with time-varying control constraints, Nonlinear Analysis: Theory, Methods and Applications, 65 (2006), 448-474. |
| [12] |
R. B. Vinter, "Optimal Control," Birkhäuser, Boston, 2000. |
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