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Distributed Decision Making and Control pp 27–53Cite as

Optimal Controller Synthesis for a Decentralized Two-Player Linear-Quadratic Regulator via Spectral Factorization

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 417))

Abstract

We develop controller synthesis algorithms for decentralized control problems. The particular system considered here consists of two interconnected linear subsystems, with communication allowed in only one direction.We develop the concept of spectral factorization, which is the approach used to construct the optimal controllers. Explicit state-space formulae are provided, and we show that each player has to do more than simply estimate the states that they cannot observe. In other words, the simplest separation principle does not hold for this decentralized control problem. Some intuition into the control policies is provided, and the order of the optimal controllers is established.

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Authors and Affiliations

  1. Department of Aeronautics and Astronautics, Stanford University, Stanford, CA, 94305, USA

    John Swigart & Sanjay Lall

Authors
  1. John Swigart
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  2. Sanjay Lall
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Editors and Affiliations

  1. Department of Automatic Control, Lund University, Ole Römers väg 1, 22100, Lund, Sweden

    Rolf Johansson

  2. Department of Automatic Control, Lund University, Ole Römers väg 1, 221 00, Lund, Sweden

    Anders Rantzer

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Swigart, J., Lall, S. (2012). Optimal Controller Synthesis for a Decentralized Two-Player Linear-Quadratic Regulator via Spectral Factorization. In: Johansson, R., Rantzer, A. (eds) Distributed Decision Making and Control. Lecture Notes in Control and Information Sciences, vol 417. Springer, London. https://doi.org/10.1007/978-1-4471-2265-4_2

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  • DOI: https://doi.org/10.1007/978-1-4471-2265-4_2

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-2264-7

  • Online ISBN: 978-1-4471-2265-4

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