Low-complexity first-order constraint linearization methods for efficient nonlinear MPC

Giampaolo Torrisi; Sergio Grammatico; Damian Frick; Tommaso Robbiani; Roy S. Smith; Manfred Morari

doi:10.1109/CDC.2017.8264304

Low-complexity first-order constraint linearization methods for efficient nonlinear MPC

Giampaolo Torrisi, Sergio Grammatico, Damian Frick, Tommaso Robbiani, Roy S. Smith, Manfred Morari

Team Bart De Schutter

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

3 Citations (Scopus)

Abstract

In this paper, we analyze first-order methods to find a KKT point of the nonlinear optimization problems arising in Model Predictive Control (MPC). The methods are based on a projected gradient and constraint linearization approach, that is, every iteration is a gradient step, projected onto a linearization of the constraints around the current iterate. We introduce an approach that uses a simple ℓ_p merit function, which has the computational advantage of not requiring any estimate of the dual variables and keeping the penalty parameter bounded. We then prove global convergence of the proposed method to a KKT point of the nonlinear problem. The first-order methods can be readily implemented in practice via the novel tool FalcOpt. The performance is then illustrated on numerical examples and compared with conventional methods.

Original language	English
Title of host publication	Proceedings of the 2017 IEEE 56th Annual Conference on Decision and Control (CDC)
Editors	A Astolfi et al
Place of Publication	Piscataway, NJ, USA
Publisher	IEEE
Pages	4376-4381
ISBN (Electronic)	978-150902873-3
DOIs	https://doi.org/10.1109/CDC.2017.8264304
Publication status	Published - 2017
Event	CDC 2017: 56th IEEE Annual Conference on Decision and Control - Melbourne, Australia Duration: 12 Dec 2017 → 15 Dec 2017 http://cdc2017.ieeecss.org/

Conference

Conference	CDC 2017: 56th IEEE Annual Conference on Decision and Control
Country/Territory	Australia
City	Melbourne
Period	12/12/17 → 15/12/17
Other	The CDC is recognized as the premier scientific and engineering conference dedicated to the advancement of the theory and practice of systems and control. The CDC annually brings together an international community of researchers and practitioners in the field of automatic control to discuss new research results, perspectives on future developments, and innovative applications relevant to decision making, systems and control, and related areas.
Internet address	http://cdc2017.ieeecss.org/

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10.1109/CDC.2017.8264304

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title = "Low-complexity first-order constraint linearization methods for efficient nonlinear MPC",

abstract = "In this paper, we analyze first-order methods to find a KKT point of the nonlinear optimization problems arising in Model Predictive Control (MPC). The methods are based on a projected gradient and constraint linearization approach, that is, every iteration is a gradient step, projected onto a linearization of the constraints around the current iterate. We introduce an approach that uses a simple ℓp merit function, which has the computational advantage of not requiring any estimate of the dual variables and keeping the penalty parameter bounded. We then prove global convergence of the proposed method to a KKT point of the nonlinear problem. The first-order methods can be readily implemented in practice via the novel tool FalcOpt. The performance is then illustrated on numerical examples and compared with conventional methods.",

author = "Giampaolo Torrisi and Sergio Grammatico and Damian Frick and Tommaso Robbiani and Smith, {Roy S.} and Manfred Morari",

year = "2017",

doi = "10.1109/CDC.2017.8264304",

language = "English",

pages = "4376--4381",

editor = "{Astolfi et al}, A",

booktitle = "Proceedings of the 2017 IEEE 56th Annual Conference on Decision and Control (CDC)",

publisher = "IEEE",

address = "United States",

note = "CDC 2017: 56th IEEE Annual Conference on Decision and Control ; Conference date: 12-12-2017 Through 15-12-2017",

url = "http://cdc2017.ieeecss.org/",

}

Torrisi, G, Grammatico, S, Frick, D, Robbiani, T, Smith, RS & Morari, M 2017, Low-complexity first-order constraint linearization methods for efficient nonlinear MPC. in A Astolfi et al (ed.), Proceedings of the 2017 IEEE 56th Annual Conference on Decision and Control (CDC). IEEE, Piscataway, NJ, USA, pp. 4376-4381, CDC 2017: 56th IEEE Annual Conference on Decision and Control, Melbourne, Australia, 12/12/17. https://doi.org/10.1109/CDC.2017.8264304

Low-complexity first-order constraint linearization methods for efficient nonlinear MPC. / Torrisi, Giampaolo; Grammatico, Sergio; Frick, Damian et al.
Proceedings of the 2017 IEEE 56th Annual Conference on Decision and Control (CDC). ed. / A Astolfi et al. Piscataway, NJ, USA: IEEE, 2017. p. 4376-4381.

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

TY - GEN

T1 - Low-complexity first-order constraint linearization methods for efficient nonlinear MPC

AU - Torrisi, Giampaolo

AU - Grammatico, Sergio

AU - Frick, Damian

AU - Robbiani, Tommaso

AU - Smith, Roy S.

AU - Morari, Manfred

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N2 - In this paper, we analyze first-order methods to find a KKT point of the nonlinear optimization problems arising in Model Predictive Control (MPC). The methods are based on a projected gradient and constraint linearization approach, that is, every iteration is a gradient step, projected onto a linearization of the constraints around the current iterate. We introduce an approach that uses a simple ℓp merit function, which has the computational advantage of not requiring any estimate of the dual variables and keeping the penalty parameter bounded. We then prove global convergence of the proposed method to a KKT point of the nonlinear problem. The first-order methods can be readily implemented in practice via the novel tool FalcOpt. The performance is then illustrated on numerical examples and compared with conventional methods.

AB - In this paper, we analyze first-order methods to find a KKT point of the nonlinear optimization problems arising in Model Predictive Control (MPC). The methods are based on a projected gradient and constraint linearization approach, that is, every iteration is a gradient step, projected onto a linearization of the constraints around the current iterate. We introduce an approach that uses a simple ℓp merit function, which has the computational advantage of not requiring any estimate of the dual variables and keeping the penalty parameter bounded. We then prove global convergence of the proposed method to a KKT point of the nonlinear problem. The first-order methods can be readily implemented in practice via the novel tool FalcOpt. The performance is then illustrated on numerical examples and compared with conventional methods.

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BT - Proceedings of the 2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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T2 - CDC 2017: 56th IEEE Annual Conference on Decision and Control

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ER -

Low-complexity first-order constraint linearization methods for efficient nonlinear MPC

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