Euler discretization for a class of nonlinear optimal control problems with control appearing linearly

Walter Alt (), Ursula Felgenhauer () and Martin Seydenschwanz ()
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Walter Alt: Friedrich-Schiller-Universität Jena
Ursula Felgenhauer: Brandenburgische Technische Universität Cottbus-Senftenberg
Martin Seydenschwanz: Siemens AG, Research in Digitalization and Automation

Computational Optimization and Applications, 2018, vol. 69, issue 3, No 9, 825-856

Abstract: Abstract We investigate Euler discretization for a class of optimal control problems with a nonlinear cost functional of Mayer type, a nonlinear system equation with control appearing linearly and constraints defined by lower and upper bounds for the controls. Under the assumption that the cost functional satisfies a growth condition we prove for the discrete solutions Hölder type error estimates w.r.t. the mesh size of the discretization. If a stronger second-order optimality condition is satisfied the order of convergence can be improved. Numerical experiments confirm the theoretical findings.

Keywords: Optimal control; Bang-bang control; Euler discretization; Error estimates; 49J15; 49M25 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-017-9969-7

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