A new approach to Lipschitz continuity in state constrained optimal control

摘要

For a linear-quadratic state constrained optimal control problem, it is proved in [11] that under an independence condition for the active constraints, the optimal control is Lipschitz continuous. We now give a new proof of this result based on an analysis of the Euler discretization given in [9]. There we exploit the Lipschitz continuity of the control to estimate the error 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. [References: 15]