On the Riccati difference equation of optimal control

Pablo A Iglesias

Research output: Contribution to journal › Article

Abstract

Necessary and sufficient conditions for the existence of a stabilizing solution to the Riccati difference equation of quadratic optimal control are derived. The results are based on a recent spectral characterization of stabilizability which allow for the time-invariant derivation to go through mutatis mutandis. It is also shown that if the system's dynamics are antistable or observable, then the solution is positive-definite.

Original languageEnglish (US)
Pages (from-to)313-326
Number of pages14
JournalLinear and Multilinear Algebra
Volume46
Issue number4
StatePublished - 1999

Fingerprint

Stabilizability
Riccati Equation
System Dynamics
Positive definite
Difference equation
Optimal Control
Necessary Conditions
Invariant
Sufficient Conditions

Keywords

  • Optimal control
  • Riccati equations
  • Time-varying systems

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On the Riccati difference equation of optimal control. / Iglesias, Pablo A.

In: Linear and Multilinear Algebra, Vol. 46, No. 4, 1999, p. 313-326.

Research output: Contribution to journal › Article

Iglesias, PA 1999, 'On the Riccati difference equation of optimal control', Linear and Multilinear Algebra, vol. 46, no. 4, pp. 313-326.
Iglesias PA. On the Riccati difference equation of optimal control. Linear and Multilinear Algebra. 1999;46(4):313-326.
Iglesias, Pablo A. / On the Riccati difference equation of optimal control. In: Linear and Multilinear Algebra. 1999 ; Vol. 46, No. 4. pp. 313-326.
@article{ba3d82728f5e4f5a9b178762a575647f,
title = "On the Riccati difference equation of optimal control",
abstract = "Necessary and sufficient conditions for the existence of a stabilizing solution to the Riccati difference equation of quadratic optimal control are derived. The results are based on a recent spectral characterization of stabilizability which allow for the time-invariant derivation to go through mutatis mutandis. It is also shown that if the system's dynamics are antistable or observable, then the solution is positive-definite.",
keywords = "Optimal control, Riccati equations, Time-varying systems",
author = "Iglesias, {Pablo A}",
year = "1999",
language = "English (US)",
volume = "46",
pages = "313--326",
journal = "Linear and Multilinear Algebra",
issn = "0308-1087",
publisher = "Taylor and Francis Ltd.",
number = "4",

}

TY - JOUR

T1 - On the Riccati difference equation of optimal control

AU - Iglesias, Pablo A

PY - 1999

Y1 - 1999

N2 - Necessary and sufficient conditions for the existence of a stabilizing solution to the Riccati difference equation of quadratic optimal control are derived. The results are based on a recent spectral characterization of stabilizability which allow for the time-invariant derivation to go through mutatis mutandis. It is also shown that if the system's dynamics are antistable or observable, then the solution is positive-definite.

AB - Necessary and sufficient conditions for the existence of a stabilizing solution to the Riccati difference equation of quadratic optimal control are derived. The results are based on a recent spectral characterization of stabilizability which allow for the time-invariant derivation to go through mutatis mutandis. It is also shown that if the system's dynamics are antistable or observable, then the solution is positive-definite.

KW - Optimal control

KW - Riccati equations

KW - Time-varying systems

UR - http://www.scopus.com/inward/record.url?scp=0000285085&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000285085&partnerID=8YFLogxK

M3 - Article

VL - 46

SP - 313

EP - 326

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 0308-1087

IS - 4

ER -

Access to Document