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Linear Quadratic Zero-Sum Two-Person Differential Games

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Encyclopedia of Systems and Control

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Abstract

As in optimal control theory, linear quadratic (LQ) differential games (DG) can be solved, even in high dimension, via a Riccati equation. However, contrary to the control case, existence of the solution of the Riccati equation is not necessary for the existence of a closed-loop saddle point. One may “survive” a particular, nongeneric, type of conjugate point. An important application of LQDGs is the so-called H ∞ -optimal control, appearing in the theory of robust control.

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Authors and Affiliations

  1. INRIA-Sophia Antipolis-Méditerranée, Sophia Antipolis, France

    Pierre Bernhard

Authors
  1. Pierre Bernhard
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Correspondence to Pierre Bernhard .

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Editors and Affiliations

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

    John Baillieul

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

    Tariq Samad

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© 2013 Springer-Verlag London

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Bernhard, P. (2013). Linear Quadratic Zero-Sum Two-Person Differential Games. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_29-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_29-1

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  • Publisher Name: Springer, London

  • Online ISBN: 978-1-4471-5102-9

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