V. Lykina, S. Pickenhain:
"Pontryagin Type Maximum Principle for budget-constrained infinite horizon optimal control problems with linear dynamics";
Journal of Mathematical Analysis and Applications, 457 (2018), 2; S. 1591 - 1612.

Kurzfassung englisch:
In this paper a class of infinite horizon optimal control problems with an isoperimetrical constraint, also interpreted as a budget constraint, is considered. Herein a linear both in the state and in the control dynamic is allowed. The problem setting includes a weighted Sobolev space as the state space. For this class of problems, we establish the necessary optimality conditions in form of a Pontryagin Type Maximum Principle including a transversality condition. The proved theoretical result is applied to a linear-quadratic regulator problem.

Budget constraint, Infinite horizon, Optimal control, Pontryagin Type Maximum Principle, Weighted Sobolev spaces, Linear-quadratic regulator

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