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

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Title: Fast and accurate method for computing non-smooth solutions to constrained control problems
Authors: Nita, L
Vila, EMG
Zagorowska, M
Kerrigan, E
Nie, Y
McInerney, I
Falugi, P
Item Type: Conference Paper
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.
Date of Acceptance: 28-Feb-2022
Publisher: IEEE
Copyright Statement: This paper is embargoed until publication.
Sponsor/Funder: Engineering & Physical Science Research Council (E
Funder's Grant Number: EGR1224-119
Conference Name: European Control Conference
Publication Status: Accepted
Start Date: 2022-07-12
Finish Date: 2022-07-15
Conference Place: London, UK
Embargo Date: This item is embargoed until publication
Appears in Collections:Electrical and Electronic Engineering