Stabilizing receding horizon H∞ controls for linear continuous time-varying systems

Ki Baek Kim; Tae Woong Yoon; Wook Hyun Kwon

doi:10.1109/9.940933

Stabilizing receding horizon H_∞ controls for linear continuous time-varying systems

Ki Baek Kim, Tae Woong Yoon, Wook Hyun Kwon

Research output: Contribution to journal › Article › peer-review

26 Citations (Scopus)

Abstract

In this note, new matrix inequality conditions on the terminal weighting matrices are proposed for linear continuous time-varying systems. Under these conditions, nonincreasing and nondecreasing monotonicities of the saddle point value of a dynamic game are shown to be guaranteed. It is proved that the proposed terminal inequality conditions ensure the closed-loop stability of the receding horizon H_∞ control (RHHC). The stabilizing RHHC guarantees the H∞ norm bound of the closed-loop system. The proposed terminal inequality conditions for the monotonicity of the saddle point value and the closed-loop stability include most well-known existing terminal conditions as special cases. The results for time-invariant systems are obtained correspondingly from those in the time-varying case.

Original language	English
Pages (from-to)	1273-1279
Number of pages	7
Journal	IEEE Transactions on Automatic Control
Volume	46
Issue number	8
DOIs	https://doi.org/10.1109/9.940933
Publication status	Published - 2001 Aug

Keywords

H control
Monotonicity
Receding horizon control
Stability

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

Access to Document

10.1109/9.940933

Cite this

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title = "Stabilizing receding horizon H∞ controls for linear continuous time-varying systems",

abstract = "In this note, new matrix inequality conditions on the terminal weighting matrices are proposed for linear continuous time-varying systems. Under these conditions, nonincreasing and nondecreasing monotonicities of the saddle point value of a dynamic game are shown to be guaranteed. It is proved that the proposed terminal inequality conditions ensure the closed-loop stability of the receding horizon H∞ control (RHHC). The stabilizing RHHC guarantees the H∞ norm bound of the closed-loop system. The proposed terminal inequality conditions for the monotonicity of the saddle point value and the closed-loop stability include most well-known existing terminal conditions as special cases. The results for time-invariant systems are obtained correspondingly from those in the time-varying case.",

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AU - Kim, Ki Baek

AU - Yoon, Tae Woong

AU - Kwon, Wook Hyun

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Y1 - 2001/8

N2 - In this note, new matrix inequality conditions on the terminal weighting matrices are proposed for linear continuous time-varying systems. Under these conditions, nonincreasing and nondecreasing monotonicities of the saddle point value of a dynamic game are shown to be guaranteed. It is proved that the proposed terminal inequality conditions ensure the closed-loop stability of the receding horizon H∞ control (RHHC). The stabilizing RHHC guarantees the H∞ norm bound of the closed-loop system. The proposed terminal inequality conditions for the monotonicity of the saddle point value and the closed-loop stability include most well-known existing terminal conditions as special cases. The results for time-invariant systems are obtained correspondingly from those in the time-varying case.

AB - In this note, new matrix inequality conditions on the terminal weighting matrices are proposed for linear continuous time-varying systems. Under these conditions, nonincreasing and nondecreasing monotonicities of the saddle point value of a dynamic game are shown to be guaranteed. It is proved that the proposed terminal inequality conditions ensure the closed-loop stability of the receding horizon H∞ control (RHHC). The stabilizing RHHC guarantees the H∞ norm bound of the closed-loop system. The proposed terminal inequality conditions for the monotonicity of the saddle point value and the closed-loop stability include most well-known existing terminal conditions as special cases. The results for time-invariant systems are obtained correspondingly from those in the time-varying case.

KW - H control

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KW - Receding horizon control

KW - Stability

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