Optimal Solutions of Linear Control Systems with Nonperiodic Convex Integrands

In this work we study the existence and asymptotic behaviour of overtaking optimal trajectories for a linear system with a nonperiodic convex cost function. We extend the results obtained by Leizarowitz (Leizarowitz, A. 1986. Tracking nonperiodic trajectories with the overtaking criterion. Appl. Math. Opt.14 155–171.) for a problem of tracking a prescribed nonperiodic trajectory with a quadratic cost function and establish the existence and uniqueness of optimal trajectories on an infinite horizon. The asymptotic dynamics of finite time optimizers is examined.