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L1 Optimal Control

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Encyclopedia of Systems and Control

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Abstract

An approach to feedback controller synthesis involves minimizing a uniform across time bound for the size of a controlled output, given a bound of the same kind for the disturbance input. In the case of linear time-invariant dynamics, this corresponds to minimizing the ℓ1 norm of the closed-loop impulse response. This optimal control problem can be recast exactly as a finite-dimensional linear program for single-input-single-output systems. On the other hand, for multiple-input-multiple-output systems, the optimal control problem can be approximated to arbitrary accuracy by a linear program of size that grows as the accuracy is improved. An overview of these results is provided in the entry below.

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Author information

Authors and Affiliations

  1. Department of Electrical & Computer Engineering, University of Minnesota Twin-Cities, Minneapolis, MN, USA

    Murti V Salapaka

Authors
  1. Murti V Salapaka
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Correspondence to Murti V Salapaka .

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, MA, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, MN, USA

    Tariq Samad

Section Editor information

  1. Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville, VIC, Australia

    Michael Cantoni

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Salapaka, M.V. (2020). L1 Optimal Control. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_100057-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_100057-1

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5102-9

  • Online ISBN: 978-1-4471-5102-9

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