Convergence analysis of euler discretization of control-state constrained optimal control problems with controls of bounded variation

Abstract

We study convergence properties of Euler discretization of optimal control problems with ordinary differential equations and mixed control-state constraints. Under suitable consistency and stability assumptions a convergence rate of order 1/p of the discretized control to the continuous control is established in the Lp-norm. Throughout it is assumed that the optimal control is of bounded variation. The convergence proof exploits the reformulation of first order necessary optimality conditions as nonsmooth equations.