Distributed Lyapunov-based MPC

R.M. Hermans, M. Lazar, A. Jokic

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

3 Citations (Scopus)

Abstract

We provide an almost decentralized solution to the problem of stabilizing a network of discrete-time nonlinear systems with coupled dynamics that are subject to local state/input constraints. By "almost decentralized" we mean that each local controller is allowed to use the states of neighboring systems for feedback, whereas it is not permitted to employ iterations between the systems in the network to compute the control action. The controller synthesis method used in this work is Lyapunov-based model predictive control. The closed-loop stability conditions are decentralized via a set of structured control Lyapunov functions (CLFs) for which the maximum over all the functions in the set is a CLF for the global network of systems. However, this does not necessarily imply that each function is a CLF for its corresponding subsystem. Additionally, a solution is provided for relaxing the temporal monotonicity of the network-wide CLF. For infinity-norm based structured CLFs and input-affine dynamics, we show that the decentralized MPC algorithm can be implemented by solving a single linear program in each network node. Two application examples are provided to illustrate the effectiveness of the developed theory and to show that the proposed method can perform as well as more complex distributed, iteration-based MPC algorithms.
LanguageEnglish
Title of host publicationDistributed model predictive control made easy
EditorsJ.M. Maestre, R.R. Negenborn
Place of PublicationBerlin
PublisherSpringer
Pages225-241
Number of pages600
ISBN (Print)978-94-007-7005-8
DOIs
StatePublished - 2014

Publication series

NameIntelligent Systems, Control and Automation
Volume69
ISSN (Print)2213-8986

Fingerprint

Lyapunov functions
Controllers
Model predictive control
Nonlinear systems
Feedback

Cite this

Hermans, R. M., Lazar, M., & Jokic, A. (2014). Distributed Lyapunov-based MPC. In J. M. Maestre, & R. R. Negenborn (Eds.), Distributed model predictive control made easy (pp. 225-241). (Intelligent Systems, Control and Automation; Vol. 69). Berlin: Springer. DOI: 10.1007/978-94-007-7006-5_14
Hermans, R.M. ; Lazar, M. ; Jokic, A./ Distributed Lyapunov-based MPC. Distributed model predictive control made easy. editor / J.M. Maestre ; R.R. Negenborn. Berlin : Springer, 2014. pp. 225-241 (Intelligent Systems, Control and Automation).
@inbook{bce565882b994777bae1d9ea3d5b738b,
title = "Distributed Lyapunov-based MPC",
abstract = "We provide an almost decentralized solution to the problem of stabilizing a network of discrete-time nonlinear systems with coupled dynamics that are subject to local state/input constraints. By {"}almost decentralized{"} we mean that each local controller is allowed to use the states of neighboring systems for feedback, whereas it is not permitted to employ iterations between the systems in the network to compute the control action. The controller synthesis method used in this work is Lyapunov-based model predictive control. The closed-loop stability conditions are decentralized via a set of structured control Lyapunov functions (CLFs) for which the maximum over all the functions in the set is a CLF for the global network of systems. However, this does not necessarily imply that each function is a CLF for its corresponding subsystem. Additionally, a solution is provided for relaxing the temporal monotonicity of the network-wide CLF. For infinity-norm based structured CLFs and input-affine dynamics, we show that the decentralized MPC algorithm can be implemented by solving a single linear program in each network node. Two application examples are provided to illustrate the effectiveness of the developed theory and to show that the proposed method can perform as well as more complex distributed, iteration-based MPC algorithms.",
author = "R.M. Hermans and M. Lazar and A. Jokic",
year = "2014",
doi = "10.1007/978-94-007-7006-5_14",
language = "English",
isbn = "978-94-007-7005-8",
series = "Intelligent Systems, Control and Automation",
publisher = "Springer",
pages = "225--241",
editor = "J.M. Maestre and R.R. Negenborn",
booktitle = "Distributed model predictive control made easy",
address = "Germany",

}

Hermans, RM, Lazar, M & Jokic, A 2014, Distributed Lyapunov-based MPC. in JM Maestre & RR Negenborn (eds), Distributed model predictive control made easy. Intelligent Systems, Control and Automation, vol. 69, Springer, Berlin, pp. 225-241. DOI: 10.1007/978-94-007-7006-5_14

Distributed Lyapunov-based MPC. / Hermans, R.M.; Lazar, M.; Jokic, A.

Distributed model predictive control made easy. ed. / J.M. Maestre; R.R. Negenborn. Berlin : Springer, 2014. p. 225-241 (Intelligent Systems, Control and Automation; Vol. 69).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

TY - CHAP

T1 - Distributed Lyapunov-based MPC

AU - Hermans,R.M.

AU - Lazar,M.

AU - Jokic,A.

PY - 2014

Y1 - 2014

N2 - We provide an almost decentralized solution to the problem of stabilizing a network of discrete-time nonlinear systems with coupled dynamics that are subject to local state/input constraints. By "almost decentralized" we mean that each local controller is allowed to use the states of neighboring systems for feedback, whereas it is not permitted to employ iterations between the systems in the network to compute the control action. The controller synthesis method used in this work is Lyapunov-based model predictive control. The closed-loop stability conditions are decentralized via a set of structured control Lyapunov functions (CLFs) for which the maximum over all the functions in the set is a CLF for the global network of systems. However, this does not necessarily imply that each function is a CLF for its corresponding subsystem. Additionally, a solution is provided for relaxing the temporal monotonicity of the network-wide CLF. For infinity-norm based structured CLFs and input-affine dynamics, we show that the decentralized MPC algorithm can be implemented by solving a single linear program in each network node. Two application examples are provided to illustrate the effectiveness of the developed theory and to show that the proposed method can perform as well as more complex distributed, iteration-based MPC algorithms.

AB - We provide an almost decentralized solution to the problem of stabilizing a network of discrete-time nonlinear systems with coupled dynamics that are subject to local state/input constraints. By "almost decentralized" we mean that each local controller is allowed to use the states of neighboring systems for feedback, whereas it is not permitted to employ iterations between the systems in the network to compute the control action. The controller synthesis method used in this work is Lyapunov-based model predictive control. The closed-loop stability conditions are decentralized via a set of structured control Lyapunov functions (CLFs) for which the maximum over all the functions in the set is a CLF for the global network of systems. However, this does not necessarily imply that each function is a CLF for its corresponding subsystem. Additionally, a solution is provided for relaxing the temporal monotonicity of the network-wide CLF. For infinity-norm based structured CLFs and input-affine dynamics, we show that the decentralized MPC algorithm can be implemented by solving a single linear program in each network node. Two application examples are provided to illustrate the effectiveness of the developed theory and to show that the proposed method can perform as well as more complex distributed, iteration-based MPC algorithms.

U2 - 10.1007/978-94-007-7006-5_14

DO - 10.1007/978-94-007-7006-5_14

M3 - Chapter

SN - 978-94-007-7005-8

T3 - Intelligent Systems, Control and Automation

SP - 225

EP - 241

BT - Distributed model predictive control made easy

PB - Springer

CY - Berlin

ER -

Hermans RM, Lazar M, Jokic A. Distributed Lyapunov-based MPC. In Maestre JM, Negenborn RR, editors, Distributed model predictive control made easy. Berlin: Springer. 2014. p. 225-241. (Intelligent Systems, Control and Automation). Available from, DOI: 10.1007/978-94-007-7006-5_14