Open-Loop Time-Consistent Solution for Equality Constrained Time-Inconsistent LQ Problem

This paper is concerned with the open-loop time-consistent solution of constrained deterministic time-inconsistent linear-quadratic (LQ) optimal control problem. The linear constraint on control may destroy the structure of the conventional LQ formulation. We successfully transformed the equality constrained LQ problem into an unconstrained LQ problem by means of partition matrix. The necessary and sufficient conditions for the existence of an open-loop time-consistent solution are also studied in this paper. And then, we give an explicit expression of the solution of the constrained LQ problem.