Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

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

  • Augusto FerranteEmail author
  • Lorenzo Ntogramatzidis
Living reference work entry

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

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 H2H 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.

Keywords

Cyclic boundary conditions Discrete-time linear systems Fixed end-point Initial value Point-to-point boundary conditions Quadratic cost Riccati equations 
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© Springer-Verlag London Ltd., part of Springer Nature 2020

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria dell’InformazioneUniversità di PadovaPadovaItaly
  2. 2.Department of Mathematics and StatisticsCurtin UniversityPerthAustralia

Section editors and affiliations

  • Michael Cantoni
    • 1
  1. 1.Department of Electrical & Electronic EngineeringThe University of MelbourneParkvilleAustralia