This article is cited in 16 papers

First-order necessary conditions in the problem of optimal control of a differential inclusion with phase constraints

A. V. Arutyunov, S. M. Aseev, V. I. Blagodatskikh

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Nondegenerate first-order necessary conditions for optimality are obtained for the problem (1.1)–(1.4) under different assumptions about controllability at the endpoints. These necessary conditions are obtained in the Hamiltonian form of Clarke [1]. With the help of a smoothing technique [2] the perturbation method in [3] is used to carry the main results in [4] (there the case when the support function $H(x,t,\psi)=\sup_{y\in F(x,t)}\langle y,\psi\rangle$ depends smoothly on the variable $x$ is considered) over to the more natural class of problems with locally Lipschitz support function $H$.

UDC: 517.9

MSC: Primary 49K24, 49K15; Secondary 34A60

Received: 15.10.1992

 English version: Russian Academy of Sciences. Sbornik. Mathematics, 1994, 79:1, 117–139

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