Fast and accurate method for computing non-smooth solutions to constrained control problems

L. Nita, E. M. G. Vila, M. A. Zagorowska, E. C. Kerrigan, Y. Nie, I. McInerney, P. Falugi

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

Abstract

Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems with constraints. State-of-the-art methods use fixed mesh schemes, which cannot achieve superlinear convergence in the presence of non-smooth solutions. In this paper, we propose using a flexible mesh in an integrated residual method. The locations of the mesh nodes are introduced as decision variables, and constraints are added to set upper and lower bounds on the size of the mesh intervals. We compare our approach to a uniform fixed mesh on a real-world satellite reorientation example. This example demonstrates that the flexible mesh enables the solver to automatically locate the discontinuities in the solution, has superlinear convergence and faster solve times, while achieving the same accuracy as a fixed mesh.

Original languageEnglish
Title of host publication2022 European Control Conference (ECC)
Pages1049-1054
Number of pages6
ISBN (Electronic)9783907144077
DOIs
Publication statusPublished - 2022
Externally publishedYes

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