Continuity and Monotonicity of the MPC Value Function with respect to Sampling Time and Prediction Horizon

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Title: Continuity and Monotonicity of the MPC Value Function with respect to Sampling Time and Prediction Horizon
Authors: Bachtiar, V
Kerrigan, EC
Moase, WH
Manzie, C
Item Type: Journal Article
Abstract: The digital implementation of model predictive control (MPC) is fundamentally governed by two design parameters; sampling time and prediction horizon. Knowledge of the properties of the value function with respect to the parameters can be used for developing optimisation tools to find optimal system designs. In particular, these properties are continuity and monotonicity. This paper presents analytical results to reveal the smoothness properties of the MPC value function in open- and closed-loop for constrained linear systems. Continuity of the value function and its differentiability for a given number of prediction steps are proven mathematically and confirmed with numerical results. Non-monotonicity is shown from the ensuing numerical investigation. It is shown that increasing sampling rate and/or prediction horizon does not always lead to an improved closedloop performance, particularly at faster sampling rates.
Issue Date: 11-Nov-2015
Date of Acceptance: 28-Sep-2015
ISSN: 1873-2836
Publisher: Elsevier
Start Page: 330
End Page: 337
Journal / Book Title: Automatica
Volume: 63
Copyright Statement: © 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Sponsor/Funder: Commission of the European Communities
Funder's Grant Number: PITN-GA-2013-607957
Keywords: Industrial Engineering & Automation
01 Mathematical Sciences
09 Engineering
08 Information And Computing Sciences
Publication Status: Published
Appears in Collections:Faculty of Engineering
Electrical and Electronic Engineering

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