TY - JOUR

T1 - Inheritance properties of the conjugate discrete-time algebraic Riccati equation

AU - Chiang, Chun Yueh

AU - Fan, Hung Yuan

N1 - Publisher Copyright:
© 2023 Elsevier Inc.

PY - 2024/2/15

Y1 - 2024/2/15

N2 - In this paper we consider a class of conjugate discrete-time Riccati equations, arising originally from the linear quadratic regulation problem for discrete-time antilinear systems. Under mild and reasonable assumptions, the existence of the maximal solution to the conjugate discrete-time Riccati equation, in which the control weighting matrix is nonsingular and its constant term is Hermitian, will be inherited to a transformed discrete-time algebraic Riccati equation. Based on this inheritance property, an accelerated fixed-point iteration is proposed for finding the maximal solution via the transformed Riccati equation. Numerical examples are shown to illustrate the correctness of our theoretical results and the feasibility of the proposed algorithm.

AB - In this paper we consider a class of conjugate discrete-time Riccati equations, arising originally from the linear quadratic regulation problem for discrete-time antilinear systems. Under mild and reasonable assumptions, the existence of the maximal solution to the conjugate discrete-time Riccati equation, in which the control weighting matrix is nonsingular and its constant term is Hermitian, will be inherited to a transformed discrete-time algebraic Riccati equation. Based on this inheritance property, an accelerated fixed-point iteration is proposed for finding the maximal solution via the transformed Riccati equation. Numerical examples are shown to illustrate the correctness of our theoretical results and the feasibility of the proposed algorithm.

KW - Antilinear system

KW - Conjugate discrete-time algebraic Riccati equation

KW - Fixed-point iteration

KW - Inheritance property

KW - LQR control problem

KW - Maximal solution

UR - http://www.scopus.com/inward/record.url?scp=85179000400&partnerID=8YFLogxK

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U2 - 10.1016/j.laa.2023.11.011

DO - 10.1016/j.laa.2023.11.011

M3 - Article

AN - SCOPUS:85179000400

SN - 0024-3795

VL - 683

SP - 71

EP - 97

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -