Optimality for Periodic Control of Functional Differential Systems

Then minimization may be performed on the interval [to, tl] only, where it is understood that x and u are periodically extended to [to, co). These periodic extensions satisfy the system equation (l.l), since x, is a complete state for this functional differential system. Hence it is sufficient to consider the optimal periodic control problem (l.l), (1.2) on [to, tI] with “mixed” boundary condition (1.3). Optimal periodic control problems for systems governed by ordinary differential equations have been studied since the 1960s where the original motivation came from chemical engineering (in particular, control of continuous stirred tank reactors). Most of the applications lie in this area and