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Finite-Horizon Linear-Quadratic Optimal Control with General Boundary Conditions

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Encyclopedia of Systems and Control

Abstract

The linear-quadratic (LQ) problem is the prototype of a large number of optimal control problems, including the fixed endpoint, the point-to-point, and several H 2∕H ∞ control problems, as well as the dual counterparts. In the past 50 years, these problems have been addressed using different techniques, each tailored to their specific structure. It is only in the last 10 years that it was recognized that a unifying framework is available. This framework hinges on formulae that parameterize the solutions of the Hamiltonian differential equation in the continuous-time case and the solutions of the extended symplectic system in the discrete-time case. Whereas traditional techniques involve the solutions of Riccati differential or difference equations, the formulae used here to solve the finite-horizon LQ control problem only rely on solutions of the algebraic Riccati equations. In this entry, aspects of the framework are described within a discrete-time context.

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Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria dell’Informazione, Università di Padova, Padova, Italy

    Augusto Ferrante

  2. Department of Mathematics and Statistics, Curtin University, Perth, WA, Australia

    Lorenzo Ntogramatzidis

Authors
  1. Augusto Ferrante
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  2. Lorenzo Ntogramatzidis
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Corresponding author

Correspondence to Augusto Ferrante .

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 & Electronic Engineering, The University of Melbourne, Parkville, VIC, Australia

    Michael Cantoni

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Ferrante, A., Ntogramatzidis, L. (2020). Finite-Horizon Linear-Quadratic Optimal Control with General Boundary Conditions. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_202-2

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_202-2

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5102-9

  • Online ISBN: 978-1-4471-5102-9

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

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Chapter history

  1. Latest

    Finite-Horizon Linear-Quadratic Optimal Control with General Boundary Conditions
    Published:
    08 November 2019

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_202-2

  2. Original

    Generalized Finite-Horizon Linear-Quadratic Optimal Control
    Published:
    18 March 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_202-1

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