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Adaptive time--mesh refinement in optimal control problems with state constraints
When are minimizing controls also minimizing relaxed controls?
1. | Imperial College London, Electrical and Electronical Engineering Department, South Kensington Campus, London SW7 2AZ, United Kingdom, United Kingdom |
References:
[1] |
F. H. Clarke, The maximum principle under minimal hypotheses, SIAM J. Control and Optim., 14 (1976), 1078-1091.
doi: 10.1137/0314067. |
[2] |
F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983, reprinted as vol. 5 of Classics in Applied Mathematics, SIAM, Philadelphia, 1990. |
[3] |
F. H. Clarke, Y. S. Ledyaev, R. J. Stern and P. R. Wolenski, Nonsmooth Analysis and Control Theory, Graduate Texts in Mathematics Vol. 178, Springer Verlag, New York, 1998. |
[4] |
A. L. Dontchev and R. T. Rockafellar, Implicit Functions and Solution Mappings: A View from Variational Analysis, Monographs in Mathematics, Springer, Berlin 2009.
doi: 10.1007/978-0-387-87821-8. |
[5] |
A. Ioffe, Euler lagrange and hamiltonian formalisms in dynamic optimization, Trans. Amer. Math. Soc., 349 (1997), 2871-2900.
doi: 10.1090/S0002-9947-97-01795-9. |
[6] |
A. Ioffe, Optimal control of differential inclusions: New developments and open problems, Proc. 41 IEEE Conference on Decision and Control, 3 (2002), 3127-3132.
doi: 10.1109/CDC.2002.1184349. |
[7] |
M. Palladino and R. B. Vinter, Minimizers that are not also relaxed minimizers, SIAM J. Control and Optim., 52 (2014), 2164-2179.
doi: 10.1137/130909627. |
[8] |
T. T. Rockafellar and J.-B. Wets, Variational Analysis, Grundlehren er Mathematischen Wissenshaft, vol. 317, Springer Verlag, New York, 1998.
doi: 10.1007/978-3-642-02431-3. |
[9] | |
[10] |
J. Warga, Normal control problems have no minimizing strictly original solutions, Bulletin of the Amer. Math. Soc., 77 (1971), 625-628.
doi: 10.1090/S0002-9904-1971-12779-9. |
[11] |
J. Warga, Optimal Control of Differential and Functional Equations, Academic Press, New York, 1972. |
[12] |
J. Warga, Controllability, extremality, and abnormality in nonsmooth optimal control, J. Optim. Theory and Applic., 41 (1983), 239-260.
doi: 10.1007/BF00934445. |
[13] |
J. Warga, Optimization and controllability without differentiability assumptions, SIAM J. Control and Optim., 21 (1983), 837-855.
doi: 10.1137/0321051. |
show all references
References:
[1] |
F. H. Clarke, The maximum principle under minimal hypotheses, SIAM J. Control and Optim., 14 (1976), 1078-1091.
doi: 10.1137/0314067. |
[2] |
F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983, reprinted as vol. 5 of Classics in Applied Mathematics, SIAM, Philadelphia, 1990. |
[3] |
F. H. Clarke, Y. S. Ledyaev, R. J. Stern and P. R. Wolenski, Nonsmooth Analysis and Control Theory, Graduate Texts in Mathematics Vol. 178, Springer Verlag, New York, 1998. |
[4] |
A. L. Dontchev and R. T. Rockafellar, Implicit Functions and Solution Mappings: A View from Variational Analysis, Monographs in Mathematics, Springer, Berlin 2009.
doi: 10.1007/978-0-387-87821-8. |
[5] |
A. Ioffe, Euler lagrange and hamiltonian formalisms in dynamic optimization, Trans. Amer. Math. Soc., 349 (1997), 2871-2900.
doi: 10.1090/S0002-9947-97-01795-9. |
[6] |
A. Ioffe, Optimal control of differential inclusions: New developments and open problems, Proc. 41 IEEE Conference on Decision and Control, 3 (2002), 3127-3132.
doi: 10.1109/CDC.2002.1184349. |
[7] |
M. Palladino and R. B. Vinter, Minimizers that are not also relaxed minimizers, SIAM J. Control and Optim., 52 (2014), 2164-2179.
doi: 10.1137/130909627. |
[8] |
T. T. Rockafellar and J.-B. Wets, Variational Analysis, Grundlehren er Mathematischen Wissenshaft, vol. 317, Springer Verlag, New York, 1998.
doi: 10.1007/978-3-642-02431-3. |
[9] | |
[10] |
J. Warga, Normal control problems have no minimizing strictly original solutions, Bulletin of the Amer. Math. Soc., 77 (1971), 625-628.
doi: 10.1090/S0002-9904-1971-12779-9. |
[11] |
J. Warga, Optimal Control of Differential and Functional Equations, Academic Press, New York, 1972. |
[12] |
J. Warga, Controllability, extremality, and abnormality in nonsmooth optimal control, J. Optim. Theory and Applic., 41 (1983), 239-260.
doi: 10.1007/BF00934445. |
[13] |
J. Warga, Optimization and controllability without differentiability assumptions, SIAM J. Control and Optim., 21 (1983), 837-855.
doi: 10.1137/0321051. |
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