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Error estimates for the Euler discretization of an optimal control problem with first-order state constraints

Joseph Frédéric Bonnans(Frederic.Bonnans***at***inria.fr)
Adriano Festa(adrianofesta***at***gmail.com)

Abstract: We study the error introduced in the solution of an optimal control problem with first order state constraints, for which the trajectories are approximated with a classical Euler scheme. We obtain order one approximation results in the $L^\infty$ norm (as opposed to the order 2/3 obtained in the literature). We assume either a strong second order optimality condition, or a weaker one in the case where the state constraint is scalar, satisfies some hypotheses for junction points, and the time step is constant. Our technique is based on some homotopy path of discrete optimal control problems that we study using perturbation analysis of nonlinear programming problems.

Keywords: Optimal control, nonlinear systems, state constraints, Euler discretization, rate of convergence.

Category 1: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Category 2: Applications -- Science and Engineering (Control Applications )

Citation: Inria Report, Dec. 2014

Download: [PDF]

Entry Submitted: 12/10/2014
Entry Accepted: 12/10/2014
Entry Last Modified: 12/10/2014

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