A deterministic linear quadratic time-inconsistent optimal control problem
Jiongmin Yong · Mathematical Control and Related Fields · 2011
A time-inconsistent optimal control problem is formulated andstudied for a controlled linear ordinary differential equation witha quadratic cost functional. A notion of time-consistent equilibriumstrategy is introduced for the original time-inconsistent problem.Under certain conditions, we construct an equilibrium strategy whichcan be represented via a Riccati--Volterra integral equation system.Our approach is based on a study of multi-person hierarchicaldifferential games.