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Synthesis of Trajectory-Dependent Control Lyapunov Functions by a Single Linear Program

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Hybrid Systems: Computation and Control (HSCC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5469))

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Abstract

Although control Lyapunov functions (CLFs) provide a mature framework for the synthesis of stabilizing controllers, their application in the field of hybrid systems remains scarce. One of the reasons for this is conservativeness of Lyapunov conditions. This article proposes a methodology that reduces conservatism of CLF design and is applicable to a wide class of discrete-time nonlinear hybrid systems. Rather than searching for global CLFs off-line, we focus on synthesizing CLFs by solving on-line an optimization problem. This approach makes it possible to derive a trajectory-dependent CLF, which is allowed to be locally non-monotone. Besides the theoretical appeal of the proposed idea, we indicate that for systems affine in control and CLFs based on infinity norms, the corresponding on-line optimization problem can be formulated as a single linear program.

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Author information

Authors and Affiliations

  1. Dept. of Electrical Eng., Eindhoven Univ. of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Mircea Lazar & Andrej Jokic

Authors
  1. Mircea Lazar
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  2. Andrej Jokic
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of California, 4531E Boelter Hall, CA 90095, Los Angeles, USA

    Rupak Majumdar

  2. Department of Electrical Engineering, University of California, 66-147F Engineering, IV Building, CA 90095-1594, Los Angeles, USA

    Paulo Tabuada

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© 2009 Springer-Verlag Berlin Heidelberg

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Lazar, M., Jokic, A. (2009). Synthesis of Trajectory-Dependent Control Lyapunov Functions by a Single Linear Program. In: Majumdar, R., Tabuada, P. (eds) Hybrid Systems: Computation and Control. HSCC 2009. Lecture Notes in Computer Science, vol 5469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00602-9_17

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  • DOI: https://doi.org/10.1007/978-3-642-00602-9_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00601-2

  • Online ISBN: 978-3-642-00602-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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