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. 
@article{TM_2008_262_a13,
     author = {N. A. Malysh},
     title = {Necessary {Optimality} {Conditions} for {Nonautonomous} {Control} {Systems} with an {Infinite} {Time} {Horizon}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {187--195},
     publisher = {mathdoc},
     volume = {262},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2008_262_a13/}
}
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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/