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A fundamental theory of deterministic linear-quadratic (LQ) control is theequivalent relationship between control problems, two-point boundary valueproblems and Riccati equations. In this paper, we extend the equivalence to ageneral time-inconsistent deterministic LQ problem, where the inconsistencyarises from non-exponential discount functions. By studying the solvability ofthe Riccati equation, we show the existence and uniqueness of the linearequilibrium for the time-inconsistent LQ problem.

On the Time-Inconsistent Deterministic Linear-Quadratic Control