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September 5, 2025Open Access

A Linear Model of Optimal Control with One-dimensional Control and State Variables

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This analysis finds solutions for discrete-time optimal control problems, suggesting necessary conditions for optimal value functions.

Optimal value functions satisfy a functional equation necessary for solving the optimization problem, and they are concave and continuous under specific conditions.
The study demonstrates existence conditions for solutions, requiring Euler and transversality conditions along with competitiveness in pay-offs.
Closed-form solutions are derived from assumptions about the control variable being concave and state transitions being strictly increasing.
The investigation includes a linear objective function within the framework of infinite-horizon optimal control problems.

Somdeb Lahiri (2025) studied this question.

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