Geodesic
The Pontryagin Maximum Principle and Transversality Conditions for an Optimal Control Problem with Infinite Time Interval
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations. Certain mathematical problems of optimal control, Tome 233 (2001), pp. 71-88

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A class of nonlinear optimal control problems with infinite time interval is investigated that arise in mathematical economics. Necessary conditions of optimality in the form of the Pontryagin maximum principle are obtained that contain additional conditions on the adjoint function and on the behavior of the Hamiltonian at infinity. In some cases, these additional conditions guarantee the validity of the usual transversality conditions at infinity. 
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     author = {S. M. Aseev and A. V. Kryazhimskii and A. M. Tarasyev},
     title = {The {Pontryagin} {Maximum} {Principle} and {Transversality} {Conditions} for an {Optimal} {Control} {Problem} with {Infinite} {Time} {Interval}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     publisher = {mathdoc},
     volume = {233},
     year = {2001},
     language = {ru},
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S. M. Aseev; A. V. Kryazhimskii; A. M. Tarasyev. The Pontryagin Maximum Principle and Transversality Conditions for an Optimal Control Problem with Infinite Time Interval. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations. Certain mathematical problems of optimal control, Tome 233 (2001), pp. 71-88. http://geodesic.mathdoc.fr/item/TM_2001_233_a1/