Second-Order Runge--Kutta Approximations in Control Constrained Optimal Control

Authors:
A. L. Dontchev;William W. Hager;Vladimir M. Veliov
Affiliations:
-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2000

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Abstract

In this paper, we analyze second-order Runge--Kutta approximations to a nonlinear optimal control problem with control constraints. If the optimal control has a derivative of bounded variation and a coercivity condition holds, we show that for a special class of Runge--Kutta schemes, the error in the discrete approximating control is O(h2) where h is the mesh spacing.