Accuracy Estimates for Bilinear Optimal Control Problems Governed by Ordinary Differential Equations. (26th April 2023)

• Record Type: Journal Article
• Authors: Körner, Jacob; Borzì, Alfio
• Is Part Of: Numerical functional analysis and optimization. Volume 44:Number 6(2023)
• Page Start: 564
• Page End: 602
• Publication Date: 2023-04-26
• Subjects: Accuracy estimates -- finite element method -- optimal control -- ordinary differential equations -- second-order optimality conditions; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2023.2192776
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: First- and second-order accuracy estimates for an optimal control problem governed by a system of ordinary differential equations with a bilinear control mechanism are presented. The numerical time discretization scheme under consideration is the finite element method with continuous piecewise linear functions. Central to this work is a first- and second-order analysis of optimality of the continuous and approximated optimal control problems. In the case of box constraints on the control, first-order error estimates for the control function are obtained assuming a piecewise constant approximation of the control, whereas second-order accuracy can be obtained in the case of a continuous, piecewise polynomial approximation. Numerical evidence is presented that supports the theoretical findings.