Geodesic
Properties of Hamiltonian Systems in the Pontryagin Maximum Principle for Economic Growth Problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control, Tome 262 (2008), pp. 127-145

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We consider an optimal control problem with a functional defined by an improper integral. We study the concavity properties of the maximized Hamiltonian and analyze the Hamiltonian systems in the Pontryagin maximum principle. On the basis of this analysis, we propose an algorithm for constructing an optimal trajectory by gluing the dynamics of the Hamiltonian systems. The algorithm is illustrated by calculating an optimal economic growth trajectory for macroeconomic data. 
@article{TM_2008_262_a9,
     author = {A. A. Krasovskii and A. M. Tarasyev},
     title = {Properties of {Hamiltonian} {Systems} in the {Pontryagin} {Maximum} {Principle} for {Economic} {Growth} {Problems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {127--145},
     publisher = {mathdoc},
     volume = {262},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2008_262_a9/}
}
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A. A. Krasovskii; A. M. Tarasyev. Properties of Hamiltonian Systems in the Pontryagin Maximum Principle for Economic Growth Problems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control, Tome 262 (2008), pp. 127-145. http://geodesic.mathdoc.fr/item/TM_2008_262_a9/