A new approach to Lipschitz continuity in state constrained optimal control

For a linear-quadratic state constrained optimal control problem, it is pro ved in [11] that under an independence condition for the active constraints , the optimal control is Lipschitz continuous. We now give a new proof of t his result based on an analysis of the Euler discretization given in [9]. T here we exploit the Lipschitz continuity of the control to estimate the err or in the Euler discretization. Here we show that the theory developed for the Euler discretization can be used to derive the Lipschitz continuity of the optimal control. (C) 1998 Elsevier Science B.V. All rights reserved.