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Continuity and monotonicity of the MPC value function with respect to sampling time and prediction horizon

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 optimization tools to find optimal system... Full description

Journal Title: Automatica January 2016, Vol.63, pp.330-337
Main Author: Bachtiar, Vincent
Other Authors: Kerrigan, Eric C. , Moase, William H. , Manzie, Chris
Format: Electronic Article Electronic Article
Language: English
Subjects:
Quelle: ScienceDirect (Elsevier B.V.)
ID: ISSN: 0005-1098 ; DOI: 10.1016/j.automatica.2015.10.042
Link: http://dx.doi.org/10.1016/j.automatica.2015.10.042
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recordid: sciversesciencedirect_elsevierS0005-1098(15)00442-2
title: Continuity and monotonicity of the MPC value function with respect to sampling time and prediction horizon
format: Article
creator:
  • Bachtiar, Vincent
  • Kerrigan, Eric C.
  • Moase, William H.
  • Manzie, Chris
subjects:
  • Control System Design
  • Optimal Control
  • Optimization
ispartof: Automatica, January 2016, Vol.63, pp.330-337
description: 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 optimization 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 closed-loop performance, particularly at faster sampling rates.
language: eng
source: ScienceDirect (Elsevier B.V.)
identifier: ISSN: 0005-1098 ; DOI: 10.1016/j.automatica.2015.10.042
fulltext: no_fulltext
issn:
  • 00051098
  • 0005-1098
url: Link


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titleContinuity and monotonicity of the MPC value function with respect to sampling time and prediction horizon
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subjectControl System Design ; Optimal Control ; Optimization
descriptionThe 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 optimization 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 closed-loop performance, particularly at faster sampling rates.
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descriptionThe 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 optimization 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 closed-loop performance, particularly at faster sampling rates.
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abstractThe 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 optimization 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 closed-loop performance, particularly at faster sampling rates.
pubElsevier Ltd
doi10.1016/j.automatica.2015.10.042
date2016-01