research-article

Error Estimates for the Euler Discretization of an Optimal Control Problem with First-Order State Constraints

Authors: J. Frédéric Bonnans,

Adriano FestaAuthors Info & Claims

SIAM Journal on Numerical Analysis, Volume 55, Issue 2

Pages 445 - 471

https://doi.org/10.1137/140999621

Published: 01 January 2017 Publication History

Abstract

We propose some error estimates for the discrete solution of an optimal control problem with first-order state constraints, where the trajectories are approximated with a classical Euler scheme. We obtain order 1 approximation results in the $L^\infty$ norm (as opposed to the order 2/3 results obtained in the literature). We assume either a strong second-order optimality condition or a weaker formulation in the case where the state constraint is scalar and satisfies some hypotheses for junction points, and where 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.

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Cited By

Martens B(2023)Error estimates for Runge–Kutta schemes of optimal control problems with index 1 DAEsComputational Optimization and Applications10.1007/s10589-023-00484-186:3(1299-1325)Online publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1007/s10589-023-00484-1
Preininger JVuong P(2018)On the convergence of the gradient projection method for convex optimal control problems with bang---bang solutionsComputational Optimization and Applications10.1007/s10589-018-9981-670:1(221-238)Online publication date: 1-May-2018
https://dl.acm.org/doi/10.1007/s10589-018-9981-6
Scarinci TVeliov V(2018)Higher-order numerical scheme for linear quadratic problems with bang---bang controlsComputational Optimization and Applications10.1007/s10589-017-9948-z69:2(403-422)Online publication date: 1-Mar-2018
https://dl.acm.org/doi/10.1007/s10589-017-9948-z

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cover image SIAM Journal on Numerical Analysis

SIAM Journal on Numerical Analysis Volume 55, Issue 2

DOI:10.1137/sjnaam.55.2

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© 2017, Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

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Published: 01 January 2017

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Cited By

Martens B(2023)Error estimates for Runge–Kutta schemes of optimal control problems with index 1 DAEsComputational Optimization and Applications10.1007/s10589-023-00484-186:3(1299-1325)Online publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1007/s10589-023-00484-1
Preininger JVuong P(2018)On the convergence of the gradient projection method for convex optimal control problems with bang---bang solutionsComputational Optimization and Applications10.1007/s10589-018-9981-670:1(221-238)Online publication date: 1-May-2018
https://dl.acm.org/doi/10.1007/s10589-018-9981-6
Scarinci TVeliov V(2018)Higher-order numerical scheme for linear quadratic problems with bang---bang controlsComputational Optimization and Applications10.1007/s10589-017-9948-z69:2(403-422)Online publication date: 1-Mar-2018
https://dl.acm.org/doi/10.1007/s10589-017-9948-z

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