Linear Control Systems with Periodic Convex Integrands

Abstract

We study the structure of approximate optimal trajectories of linear control systems with periodic convex integrands and show that these systems possess a turnpike property. To have this property means, roughly speaking, that the approximate optimal trajectories are determined mainly by the integrand, and are essentially independent of the choice of time interval and data, except in regions close to the endpoints of the time interval. We also show the stability of the turnpike phenomenon under small perturbations of integrands and study the structure of approximate optimal trajectories in regions close to the endpoints of the time intervals.