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Modeling round-off error in the fast gradient method for predictive control

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Title: Modeling round-off error in the fast gradient method for predictive control
Authors: McInerney, I
Kerrigan, E
Constantinides, G
Item Type: Conference Paper
Abstract: We present a method for determining the smallest precision required to have algorithmic stability of an implementation of the Fast Gradient Method (FGM) when solving a linear Model Predictive Control (MPC) problem in fixed-point arithmetic. We derive two models for the round-off error present in fixed-point arithmetic. The first is a generic model with no assumptions on the predicted system or weight matrices. The second is a parametric model that exploits the Toeplitz structure of the MPC problem for a Schur-stable system. We also propose a metric for measuring the amount of round-off error the FGM iteration can tolerate before becoming unstable. This metric is combined with the round-off error models to compute the minimum number of fractional bits needed for the fixed-point data type. Using these models, we show that exploiting the MPC problem structure nearly halves the number of fractional bits needed to implement an example problem. We show that this results in significant decreases in resource usage, computational energy and execution time for an implementation on a Field Programmable Gate Array.
Issue Date: 12-Mar-2020
Date of Acceptance: 19-Jul-2019
URI: http://hdl.handle.net/10044/1/73269
DOI: 10.1109/CDC40024.2019.9029910
Publisher: IEEE
Start Page: 1
End Page: 6
Journal / Book Title: 2019 IEEE 58th Conference on Decision and Control (CDC)
Copyright Statement: © 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Conference Name: 2019 IEEE 58th Conference on Decision and Control (CDC)
Keywords: Science & Technology
Automation & Control Systems
Engineering, Electrical & Electronic
Publication Status: Published
Start Date: 2019-12-11
Finish Date: 2019-12-13
Conference Place: Nice, France
Online Publication Date: 2020-03-12
Appears in Collections:Electrical and Electronic Engineering
Faculty of Engineering