New results on stability margins of nonlinear discrete-time receding horizon h control

Choon Ki Ahn, Moon Kyou Song

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper, we present some new results on stability margins of receding horizon H control for nonlinear discrete-time systems with disturbance. First, we propose a nonlinear inequality condition on the terminal cost for nonlinear discrete-time systems with disturbance. Under this condition, noninceasing monotonicity of the saddle point value function of the finite horizon dynamic game is shown to be guaranteed. We show that the derived condition on the terminal cost ensures closed-loop internal stability. The proposed receding horizon H control guarantees the infinite horizon H norm bound of the closed-loop system. Under additional conditions, the global result and the input-to-state stable (ISS) property of the proposed receding horizon controller are also given. Finally, we derive new H stability and ISS margins for the proposed receding horizon controller. The proposed result has a larger stability region than the existing inverse optimality based results.

Original languageEnglish
Pages (from-to)1703-1713
Number of pages11
JournalInternational Journal of Innovative Computing, Information and Control
Volume9
Issue number4
Publication statusPublished - 2013 May 21

Fingerprint

Stability Margin
Horizon
Discrete-time
Nonlinear Discrete-time Systems
Disturbance
Controller
Controllers
Dynamic Games
Stability Region
Finite Horizon
Infinite Horizon
Costs
Saddlepoint
Closed loop systems
Value Function
Margin
Closed-loop
Closed-loop System
Monotonicity
Optimality

Keywords

  • Control
  • Discrete-time
  • H
  • Input-to-state stability (ISS)
  • Nonlinear systems
  • Receding horizon control (RHC)
  • Stability margin

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Information Systems
  • Software
  • Theoretical Computer Science

Cite this

New results on stability margins of nonlinear discrete-time receding horizon h control. / Ahn, Choon Ki; Song, Moon Kyou.

In: International Journal of Innovative Computing, Information and Control, Vol. 9, No. 4, 21.05.2013, p. 1703-1713.

Research output: Contribution to journalArticle

@article{4ad7ee9d3d2e431cb12b0c31f55a5583,
title = "New results on stability margins of nonlinear discrete-time receding horizon h∞ control",
abstract = "In this paper, we present some new results on stability margins of receding horizon H∞ control for nonlinear discrete-time systems with disturbance. First, we propose a nonlinear inequality condition on the terminal cost for nonlinear discrete-time systems with disturbance. Under this condition, noninceasing monotonicity of the saddle point value function of the finite horizon dynamic game is shown to be guaranteed. We show that the derived condition on the terminal cost ensures closed-loop internal stability. The proposed receding horizon H∞ control guarantees the infinite horizon H∞ norm bound of the closed-loop system. Under additional conditions, the global result and the input-to-state stable (ISS) property of the proposed receding horizon controller are also given. Finally, we derive new H∞ stability and ISS margins for the proposed receding horizon controller. The proposed result has a larger stability region than the existing inverse optimality based results.",
keywords = "Control, Discrete-time, H, Input-to-state stability (ISS), Nonlinear systems, Receding horizon control (RHC), Stability margin",
author = "Ahn, {Choon Ki} and Song, {Moon Kyou}",
year = "2013",
month = "5",
day = "21",
language = "English",
volume = "9",
pages = "1703--1713",
journal = "International Journal of Innovative Computing, Information and Control",
issn = "1349-4198",
publisher = "IJICIC Editorial Office",
number = "4",

}

TY - JOUR

T1 - New results on stability margins of nonlinear discrete-time receding horizon h∞ control

AU - Ahn, Choon Ki

AU - Song, Moon Kyou

PY - 2013/5/21

Y1 - 2013/5/21

N2 - In this paper, we present some new results on stability margins of receding horizon H∞ control for nonlinear discrete-time systems with disturbance. First, we propose a nonlinear inequality condition on the terminal cost for nonlinear discrete-time systems with disturbance. Under this condition, noninceasing monotonicity of the saddle point value function of the finite horizon dynamic game is shown to be guaranteed. We show that the derived condition on the terminal cost ensures closed-loop internal stability. The proposed receding horizon H∞ control guarantees the infinite horizon H∞ norm bound of the closed-loop system. Under additional conditions, the global result and the input-to-state stable (ISS) property of the proposed receding horizon controller are also given. Finally, we derive new H∞ stability and ISS margins for the proposed receding horizon controller. The proposed result has a larger stability region than the existing inverse optimality based results.

AB - In this paper, we present some new results on stability margins of receding horizon H∞ control for nonlinear discrete-time systems with disturbance. First, we propose a nonlinear inequality condition on the terminal cost for nonlinear discrete-time systems with disturbance. Under this condition, noninceasing monotonicity of the saddle point value function of the finite horizon dynamic game is shown to be guaranteed. We show that the derived condition on the terminal cost ensures closed-loop internal stability. The proposed receding horizon H∞ control guarantees the infinite horizon H∞ norm bound of the closed-loop system. Under additional conditions, the global result and the input-to-state stable (ISS) property of the proposed receding horizon controller are also given. Finally, we derive new H∞ stability and ISS margins for the proposed receding horizon controller. The proposed result has a larger stability region than the existing inverse optimality based results.

KW - Control

KW - Discrete-time

KW - H

KW - Input-to-state stability (ISS)

KW - Nonlinear systems

KW - Receding horizon control (RHC)

KW - Stability margin

UR - http://www.scopus.com/inward/record.url?scp=84877825496&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84877825496&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84877825496

VL - 9

SP - 1703

EP - 1713

JO - International Journal of Innovative Computing, Information and Control

JF - International Journal of Innovative Computing, Information and Control

SN - 1349-4198

IS - 4

ER -