Necessary Conditions for Impulsive Nonlinear Optimal Control Problems without a priori Normality Assumptions |
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| Authors: | A Arutyunov V Dykhta F Lobo Pereira |
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| Institution: | (1) Department of Differential Equations and Functional Analysis, People Friendship University of Russia, Moscow, Russia;(2) Department of Mathematics, Baikal State University of Economy and Law, Irkutsk, Russia;(3) Department of Electrotechnical and Computer Engineering, Faculty of Engineering, University of Porto, Porto, Portugal |
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| Abstract: | First-order and second-order necessary conditions of optimality for an impulsive control problem that remain informative for abnormal control processes are presented and derived. One of the main features of these conditions is that no a priori normality assumptions are required. This feature follows from the fact that these conditions rely on an extremal principle which is proved for an abstract minimization problem with equality constraints, inequality constraints, and constraints given by an inclusion in a convex cone. Two simple examples illustrate the power of the main result.The first author was partially supported by the Russian Foundation for Basic Research Grant 02-01-00334. The second author was partially supported by the Russian Foundation for Basic Research Grant 00-01-00869. The third author was partially supported by Fundacao para a Ciencia e Tecnologia and by INVOTAN Grant. |
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| Keywords: | Optimal impulsive control extremal principle second order optimality conditions abnormality |
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