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

Optimality Conditions and the Hamiltonian for a Distributed Optimal Control Problem on Controlled... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

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

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Publisher
Springer US
Copyright
Copyright © 2014 by Springer Science+Business Media New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-014-9237-5
Publisher site
See Article on Publisher Site

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