Linear quadratic regulation for discrete-time antilinear systems: An anti-Riccati matrix equation approach

Ai Guo WU; Yang-Yang QIAN; Wanquan LIU; Victor SREERAM

doi:10.1016/j.jfranklin.2015.02.023

Linear quadratic regulation for discrete-time antilinear systems: An anti-Riccati matrix equation approach

Ai Guo WU
, Yang-Yang QIAN^*
, Wanquan LIU
, Victor SREERAM

^*Corresponding author for this work

Research output: Journal Publications › Journal Article (refereed) › peer-review

19 Citations (Scopus)

Abstract

In this paper, the linear quadratic regulation problem is investigated for discrete-time antilinear systems. Two cases are considered: finite time state regulation and infinite time state regulation. First, the discrete minimum principle is generalized to the complex domain. By using the discrete minimum principle and dynamic programming, necessary and sufficient conditions for the existence of the unique optimal control are obtained for the finite time regulation problem in terms of the so-called anti-Riccati matrix equation. Besides, the optimal value of the performance index under the optimal control is provided. Furthermore, the optimal regulation problem on an infinite interval is investigated under the assumption that the considered time-invariant antilinear system is controllable. The resulted closed-loop system under the optimal control turns out to be asymptotically stable.

Original language	English
Pages (from-to)	1041-1060
Number of pages	20
Journal	Journal of the Franklin Institute
Volume	353
Issue number	5
Early online date	6 Mar 2015
DOIs	https://doi.org/10.1016/j.jfranklin.2015.02.023
Publication status	Published - Mar 2016
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2015 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Funding

This work is supported by the Project for Distinguished Young Scholars of the Basic Research Plan in Shenzhen City under Contract no. JCJ201110001 , by the National Natural Science Foundation of China under Grant nos. 61273094 and 61203125 , by Specialized Research Fund for the Doctoral Program of Higher Education under Grant no. 20132302110053 and by the Foundation for Creative Research Groups of the National Natural Science Foundation of China under Grant no. 61321062 .

Access to Document

10.1016/j.jfranklin.2015.02.023

Cite this

@article{7171f221cb1f481881964342caaf4dc6,

title = "Linear quadratic regulation for discrete-time antilinear systems: An anti-Riccati matrix equation approach",

abstract = "In this paper, the linear quadratic regulation problem is investigated for discrete-time antilinear systems. Two cases are considered: finite time state regulation and infinite time state regulation. First, the discrete minimum principle is generalized to the complex domain. By using the discrete minimum principle and dynamic programming, necessary and sufficient conditions for the existence of the unique optimal control are obtained for the finite time regulation problem in terms of the so-called anti-Riccati matrix equation. Besides, the optimal value of the performance index under the optimal control is provided. Furthermore, the optimal regulation problem on an infinite interval is investigated under the assumption that the considered time-invariant antilinear system is controllable. The resulted closed-loop system under the optimal control turns out to be asymptotically stable.",

author = "WU, \{Ai Guo\} and Yang-Yang QIAN and Wanquan LIU and Victor SREERAM",

year = "2016",

month = mar,

doi = "10.1016/j.jfranklin.2015.02.023",

language = "English",

volume = "353",

pages = "1041--1060",

journal = "Journal of the Franklin Institute",

issn = "0016-0032",

publisher = "Elsevier Ltd",

number = "5",

}

TY - JOUR

T1 - Linear quadratic regulation for discrete-time antilinear systems: An anti-Riccati matrix equation approach

AU - WU, Ai Guo

AU - QIAN, Yang-Yang

AU - LIU, Wanquan

AU - SREERAM, Victor

PY - 2016/3

Y1 - 2016/3

N2 - In this paper, the linear quadratic regulation problem is investigated for discrete-time antilinear systems. Two cases are considered: finite time state regulation and infinite time state regulation. First, the discrete minimum principle is generalized to the complex domain. By using the discrete minimum principle and dynamic programming, necessary and sufficient conditions for the existence of the unique optimal control are obtained for the finite time regulation problem in terms of the so-called anti-Riccati matrix equation. Besides, the optimal value of the performance index under the optimal control is provided. Furthermore, the optimal regulation problem on an infinite interval is investigated under the assumption that the considered time-invariant antilinear system is controllable. The resulted closed-loop system under the optimal control turns out to be asymptotically stable.

AB - In this paper, the linear quadratic regulation problem is investigated for discrete-time antilinear systems. Two cases are considered: finite time state regulation and infinite time state regulation. First, the discrete minimum principle is generalized to the complex domain. By using the discrete minimum principle and dynamic programming, necessary and sufficient conditions for the existence of the unique optimal control are obtained for the finite time regulation problem in terms of the so-called anti-Riccati matrix equation. Besides, the optimal value of the performance index under the optimal control is provided. Furthermore, the optimal regulation problem on an infinite interval is investigated under the assumption that the considered time-invariant antilinear system is controllable. The resulted closed-loop system under the optimal control turns out to be asymptotically stable.

UR - https://www.scopus.com/pages/publications/84925308599

U2 - 10.1016/j.jfranklin.2015.02.023

DO - 10.1016/j.jfranklin.2015.02.023

M3 - Journal Article (refereed)

AN - SCOPUS:84925308599

SN - 0016-0032

VL - 353

SP - 1041

EP - 1060

JO - Journal of the Franklin Institute

JF - Journal of the Franklin Institute

IS - 5

ER -

Linear quadratic regulation for discrete-time antilinear systems: An anti-Riccati matrix equation approach

Abstract

Bibliographical note

Funding

Access to Document

Other files and links

Fingerprint

Cite this