Suboptimal Solution of a Cheap Control Problem for Linear Systems with Multiple State Delays

Abstract

A finite-horizon linear-quadratic optimal control problem with multiple pointwise and distributed state delays in the dynamics is considered. The control cost in the performance index is small with respect to the state cost. An asymptotic solution of the singularly perturbed set of Riccati-type functional-differential equations, associated with the original control problem by the optimality conditions, is constructed and justified. Based on this solution, two types of suboptimal feedback control for the original problem are derived. These suboptimal controls are justified for two classes of the initial condition for the state variable.