On the Essential Boundedness of Solutions to Problems in Piecewise Linear-quadratic Optimal Control

Primal and dual problems of optimal control with linear, quadratic or piecewise linear-quadratic convex objective are considered in which a linear dynamical system is subjected to linear inequality constraints that could jointly involve states and controls. It is shown that when such constraints, except for the ones on controls only, are represented by penalty terms, and a mild coercivity condition is satisfied, the optimal controls for both problems will be essentially bounded in time. The optimal trajectories will thus be Lipschitzian. * This research was supported in part by a grant from the National Science Foundation at the University of Washington, Seattle