State constrained optimal control of linear time-varying systems

Abstract

A state constrained optimal control problem subject to continuous-time linear time-varying dynamics is decomposed into a family of linear quadratic regulator (LQR) problems via convex duality and a game formalism. By addressing these LQR problems directly, a feedback characterisation for the optimal control is given in terms of the solution of a two-point boundary value problem (TPBVP). This characterisation is illustrated via its application in a simple example.