Geodesic
First-order necessary conditions in the problem of optimal control of a differential inclusion with phase constraints
Sbornik. Mathematics, Tome 79 (1994) no. 1, pp. 117-139 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $H$. 
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A. V. Arutyunov; S. M. Aseev; V. I. Blagodatskikh. First-order necessary conditions in the problem of optimal control of a differential inclusion with phase constraints. Sbornik. Mathematics, Tome 79 (1994) no. 1, pp. 117-139. http://geodesic.mathdoc.fr/item/SM_1994_79_1_a8/

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