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Distributed Lyapunov-Based MPC

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Distributed Model Predictive Control Made Easy

Part of the book series: Intelligent Systems, Control and Automation: Science and Engineering ((ISCA,volume 69))

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.

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Notes

  1. 1.

    For example, in electrical power systems, where a dynamical system is a power generator, the interconnection signal is the generator bus voltage and line power (or current) flow in the corresponding power line, which can be directly measured.

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Acknowledgments

This research is supported by the Veni grant “Flexible Lyapunov Functions for Real-time Control”, grant number 10230, awarded by STW (Dutch Science Foundation) and NWO (The Netherlands Organization for Scientific Research), and is part of the EOS-LT Regelduurzaam project (funded by the Dutch Ministry of Economic Affairs) and the European Commission Research Project FP7–ICT–249096 “Price-based Control of Electrical Power Systems” (E-Price).

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Authors and Affiliations

  1. Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    R. Hermans & M. Lazar

  2. Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, Croatia

    A. Jokić

Authors
  1. R. Hermans
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  2. M. Lazar
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  3. A. Jokić
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Corresponding author

Correspondence to R. Hermans .

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Editors and Affiliations

  1. Systems Engineering and Automation Dept, University of Seville, Seville, Spain

    José M. Maestre

  2. Dept of Marine & Transport Technology, Delft University of Technology, Delft, The Netherlands

    Rudy R. Negenborn

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Hermans, R., Lazar, M., Jokić, A. (2014). Distributed Lyapunov-Based MPC. In: Maestre, J., Negenborn, R. (eds) Distributed Model Predictive Control Made Easy. Intelligent Systems, Control and Automation: Science and Engineering, vol 69. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7006-5_14

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  • DOI: https://doi.org/10.1007/978-94-007-7006-5_14

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  • Publisher Name: Springer, Dordrecht

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  • Online ISBN: 978-94-007-7006-5

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