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 control system with a nonperiodic convex cost function. We extend the results obtained by Leizarowitz 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.