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“Piecewise quadratic Lyapunov functions for stability verification of approximate explicit MPC”

Authors: Morten Hovd and Sorin Olaru,
Affiliation: NTNU, Department of Engineering Cybernetics and SUPELEC Systems Sciences (France)
Reference: 2010, Vol 31, No 2, pp. 45-53.

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Keywords: Piecewise Quadratic Lyapunov function, Linear Matrix Inequalities, Model Predictive Control, Piecewise Affine Systems

Abstract: Explicit MPC of constrained linear systems is known to result in a piecewise affine controller and therefore also piecewise affine closed loop dynamics. The complexity of such analytic formulations of the control law can grow exponentially with the prediction horizon. The suboptimal solutions offer a trade-off in terms of complexity and several approaches can be found in the literature for the construction of approximate MPC laws. In the present paper a piecewise quadratic (PWQ) Lyapunov function is used for the stability verification of an of approximate explicit Model Predictive Control (MPC). A novel relaxation method is proposed for the LMI criteria on the Lyapunov function design. This relaxation is applicable to the design of PWQ Lyapunov functions for discrete-time piecewise affine systems in general.

PDF PDF (337 Kb)        DOI: 10.4173/mic.2010.2.1



DOI forward links to this article:
  [1] W.P.M.H. Heemels, B.A.G. Genuit and L. Lu (2012), doi:10.1049/iet-cta.2010.0709
  [2] Hoai-Nam Nguyen, Sorin Olaru and Morten Hovd (2012), doi:10.1080/00207179.2012.713516
  [3] Ionela Prodan, Sorin Olaru, Ricardo Bencatel, Joo Borges de Sousa, Cristina Stoica and Silviu-Iulian Niculescu (2013), doi:10.1016/j.conengprac.2013.05.010
  [4] Morten Hovd and Sorin Olaru (2013), doi:10.1016/j.automatica.2012.10.013
  [5] S. Olaru, N. A. Nguyen, G. Bitsoris, P. Rodriguez-Ayerbe and M. Hovd (2013), doi:10.1109/ICSTCC.2013.6688989
  [6] Insu Chang and Joseph Bentsman (2015), doi:10.1109/CDC.2015.7402821
  [7] Yasuaki Oishi (2012), doi:10.3182/20120620-3-DK-2025.00174
  [8] Richard Oberdieck, Nikolaos A. Diangelakis, Ioana Nascu, Maria M. Papathanasiou, Muxin Sun, Styliani Avraamidou and Efstratios N. Pistikopoulos (2016), doi:10.1016/j.cherd.2016.09.034


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BibTeX:
@article{MIC-2010-2-1,
  title={{Piecewise quadratic Lyapunov functions for stability verification of approximate explicit MPC}},
  author={Hovd, Morten and Olaru, Sorin},
  journal={Modeling, Identification and Control},
  volume={31},
  number={2},
  pages={45--53},
  year={2010},
  doi={10.4173/mic.2010.2.1},
  publisher={Norwegian Society of Automatic Control}
};

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