On constrained impulsive control problems
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This paper considers constrained impulsive control problems for which the authors propose a new mathematical concept of control required for the impulsive framework. These controls can arise in engineering, in particular, in problems of space navigation. We derive necessary extremum conditions in the form of the Pontryagin maximum principle and also study conditions under which the constraint regularity clarifications become weaker. In the proof of the main result, Ekeland’s variational principle is used.
KeywordsRadon Optimal Control Problem Multivalued Mapping Impulsive Control Pontryagin Maximum Principle
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- 1.V. M. Alekseev, V. M. Tikhomirov, and S. V. Fomin, Optimal Control [in Russian], Nauka, Moscow (1983).Google Scholar
- 2.A. V. Arutyunov, Optimality Conditions: Abnormal and Degenerate Problems, Kluwer Academic Publisher (2000).Google Scholar
- 3.A. V. Arutyunov, “Some properties of quadratic mappings,” Vestn. MGU, Vychisl. Mat. Kibern., 2, 30–32 (1999).Google Scholar
- 4.A. V. Arutyunov and D. Yu. Karamzin, “Necessary conditions of the minimum in an impulse optimal control problem,” In: Nonlinear Dynamics and Control [in Russian], 4, Fizmatlit, Moscow (2004), pp. 205–240.Google Scholar
- 6.A. V. Arutyunov, D. Yu. Karamzin, and F. L. Pereira, “Maximum principle in problems with mixed constraints under weak assumptions of regularity,” In: Theoretical and Applied Problems of Nonlinear Analysis [in Russian], Computational Center of Russian Academy of Sciences (2008), pp. 1–33.Google Scholar
- 7.A. V. Arutyunov, D. Yu. Karamzin, and F. L. Pereira, “Necessary optimality conditions for problems with equality and inequality constraints: The abnormal case,” J. Optim. Theory Appl., 1 (2009) (in press).Google Scholar
- 11.V. A. Dykhta and O. N. Samsonyuk, Optimal Impulse Control with Applications [in Russian], Fizmatlit, Moscow (2000).Google Scholar
- 16.A. B. Kurzhanskii, Optimal Systems with Impulse Controls, Differential Games and Control Problems [in Russian], Preprint, UNTs, Akad. Nauk SSSR, Sverdlovsk, 131–156 (1975).Google Scholar
- 18.A. A. Milyutin, Maximum Principle in a General Optimal Control Problem [in Russian], Fizmatlit, Moscow (2001).Google Scholar
- 19.B. S. Mordukhovich, Variational Analysis and Generalized Differentiation, Springer (2005).Google Scholar
- 24.R. Rockafellar, Convex Analysis, Princeton University Press (1970).Google Scholar