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Optimality Conditions and the Hamiltonian for a Distributed Optimal Control Problem on Controlled Domain

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Abstract

The paper investigates an optimal control problem for a distributed system arising in the economics of endogenous growth. The problem involves a specific coupled family of controlled ODEs parameterized by a parameter (representing the heterogeneity) running over a domain that may dynamically depend on the control and on the state of the system. Existence of an optimal control is obtained and continuity of any optimal control with respect to the parameter of heterogeneity is proved. The latter allows to substantially strengthen previously obtained necessary optimality conditions and to obtain a Pontryagin’s type maximum principle. The necessary optimality conditions obtained here have a Hamiltonian representation, and stationarity of the Hamiltonian along any optimal trajectory is proved in the case of time-independent data.

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Acknowledgments

This research was funded by the Austrian Science Foundation (FWF) under Grant No I 476-N13.

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Authors and Affiliations

  1. ORCOS, Institute of Mathematical Methods in Economics, Vienna University of Technology, Argentinierstrasse 8/105-4, 1040 , Vienna, Austria

    Bernhard Skritek & Vladimir M. Veliov

  2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., Block 8, 1113 , Sofia, Bulgaria

    Tsvetomir Tsachev

Authors
  1. Bernhard Skritek
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  2. Tsvetomir Tsachev
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  3. Vladimir M. Veliov
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Correspondence to Tsvetomir Tsachev.

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Skritek, B., Tsachev, T. & Veliov, V.M. Optimality Conditions and the Hamiltonian for a Distributed Optimal Control Problem on Controlled Domain. Appl Math Optim 70, 141–164 (2014). https://doi.org/10.1007/s00245-014-9237-5

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  • DOI: https://doi.org/10.1007/s00245-014-9237-5

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