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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 2, Pages 220–236 (Mi zvmmf179)  
Minimizing sequences in optimal control with approximately given input data and the regularizing properties of the Pontryagin maximum principle

M. I. Sumin, E. V. Trushina

Nizhni Novgorod State University, pr. Gagarina 23, Nizhni Novgorod, 603950, Russia
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Abstract: Results related to the optimal control theory for systems with approximately given input data are presented. The basic (desired) element in the theory is the minimizing sequence of feasible controls rather than the classical optimal control. Necessary and sufficient conditions for minimizing sequences are established. The regularizing properties of the Pontryagin maximum principle and of minimizing sequences are discussed. Three basic regularization levels are singled out that are characteristic of any optimal control problem. The stability of the optimal value in a problem depending on the constraint parameter is discussed. Illustrative examples are considered in detail.
Key words: optimal control, approximately given input data, parametric problem, necessary and sufficient conditions, minimizing sequence, Pontryagin maximum principle.
Received: 22.05.2007
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 2, Pages 209–224
DOI: https://doi.org/10.1007/s11470-008-2005-3
Bibliographic databases:
Document Type: Article
UDC: 519.626
Language: Russian
Citation: M. I. Sumin, E. V. Trushina, “Minimizing sequences in optimal control with approximately given input data and the regularizing properties of the Pontryagin maximum principle”, Zh. Vychisl. Mat. Mat. Fiz., 48:2 (2008), 220–236; Comput. Math. Math. Phys., 48:2 (2008), 209–224
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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