  A fundamental theory of deterministic linear-quadratic (LQ) control is the
equivalent relationship between control problems, two-point boundary value
problems and Riccati equations. In this paper, we extend the equivalence to a
general time-inconsistent deterministic LQ problem, where the inconsistency
arises from non-exponential discount functions. By studying the solvability of
the Riccati equation, we show the existence and uniqueness of the linear
equilibrium for the time-inconsistent LQ problem.
