Continuity and Monotonicity of the MPC Value Function with respect to Sampling Time and Prediction Horizon
File(s)
Accepted version
Author(s)
Bachtiar, V
Kerrigan, EC
Moase, WH
Manzie, C
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.
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.
Date Issued
2015-11-11
Date Acceptance
2015-09-28
Citation
Automatica, 2015, 63, pp.330-337
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 http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor
Commission of the European Communities
Grant Number
PITN-GA-2013-607957
Subjects
Industrial Engineering & Automation
01 Mathematical Sciences
09 Engineering
08 Information And Computing Sciences
Publication Status
Published