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B. Skritek, Tz. Tsachev, V.M. Veliov:
"Optimality conditions and the Hamiltonian for a distributed optimal control problem on controlled domain";
Applied Mathematics and Optimization, 70 (2014), 1; S. 141 - 164.

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.

Optimal control · Distributed control · Controlled domain · Pontryagintype maximum principle · Endogenous economic growth

http://dx.doi.org/10.1007/s00245-014-9237-5