Geodesic
Necessary Optimality Conditions for Nonautonomous Control Systems with an Infinite Time Horizon
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control, Tome 262 (2008), pp. 187-195.

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We consider a nonautonomous optimal control problem on an infinite time horizon with an integral functional containing a positive discounting factor. In the case of a dominating discounting factor, we obtain a variant of the Pontryagin maximum principle that contains explicit expressions for the adjoint variable and the Hamiltonian of the problem. 
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N. A. Malysh. Necessary Optimality Conditions for Nonautonomous Control Systems with an Infinite Time Horizon. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control, Tome 262 (2008), pp. 187-195. http://geodesic.mathdoc.fr/item/TM_2008_262_a13/

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