Abstract
A survey on the theory of maximum principle for state-constrained optimal control problems is presented. The focus is on such issues as regularity and controllability conditions, non-degeneracy and normality of the maximum principle, and on the continuity of the measure multiplier.
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Notes
The set U can be an arbitrary subset of \(\mathbb {R}^m\). However, with regard to the application aspects of the control theory, in much work on this theory, it is considered closed.
Let us remark that such aspects as reducing the smoothness, or continuity, hypothesis for the data are not the concern of the present survey.
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Acknowledgements
The authors are grateful to the anonymous reviewers for their valuable remarks which significantly improved the exposition. The work of the first author (Sects. 2, 3) was supported by the Russian Science Foundation, Project No. 17-11-01168. The work of the second author (Sects. 4, 5) was supported by the Russian Science Foundation, Project No. 19-11-00258 carried out in the Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow, Russia.
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Arutyunov, A., Karamzin, D. A Survey on Regularity Conditions for State-Constrained Optimal Control Problems and the Non-degenerate Maximum Principle. J Optim Theory Appl 184, 697–723 (2020). https://doi.org/10.1007/s10957-019-01623-7
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DOI: https://doi.org/10.1007/s10957-019-01623-7