An Algebraic Formula for Performance Bounds of a Weighted H∞ Optimal Control Problem

Andres A. Peters; Francisco Vargas; Jie Chen

doi:10.1109/TAC.2020.2982135

An Algebraic Formula for Performance Bounds of a Weighted H_∞ Optimal Control Problem

Andres A. Peters^*, Francisco Vargas, Jie Chen

^*Corresponding author for this work

Department of Electrical Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

2 Citations (Scopus)

Abstract

This note provides performance bounds for a particular H_∞ model matching problem. We consider scalar linear time invariant (LTI) plants in an one degree-of-freedom control loop. We obtained explicit expressions for the Gramians needed when Nehari's Theorem is applied to this problem, leading to a simple algebraic equation for the optimal performance. This formula sheds light upon the effect that non-minimum phase zeros have on the optimal performance, and yields easily computable bounds and approximations.

Original language	English
Article number	9042269
Pages (from-to)	781-786
Number of pages	6
Journal	IEEE Transactions on Automatic Control
Volume	66
Issue number	2
Online published	19 Mar 2020
DOIs	https://doi.org/10.1109/TAC.2020.2982135
Publication status	Published - Feb 2021

Research Keywords

H∞ control
Discrete-time systems
Performance bounds

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10.1109/TAC.2020.2982135

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AB - This note provides performance bounds for a particular H∞ model matching problem. We consider scalar linear time invariant (LTI) plants in an one degree-of-freedom control loop. We obtained explicit expressions for the Gramians needed when Nehari's Theorem is applied to this problem, leading to a simple algebraic equation for the optimal performance. This formula sheds light upon the effect that non-minimum phase zeros have on the optimal performance, and yields easily computable bounds and approximations.

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JF - IEEE Transactions on Automatic Control

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ER -

An Algebraic Formula for Performance Bounds of a Weighted H_∞ Optimal Control Problem

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Research Keywords

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GRF: Bode Integrals and Power Gain Bounds for Disturbance Attenuation of MIMO Networked Control Systems

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An Algebraic Formula for Performance Bounds of a Weighted H∞ Optimal Control Problem

Abstract

Research Keywords

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GRF: Bode Integrals and Power Gain Bounds for Disturbance Attenuation of MIMO Networked Control Systems

Cite this

An Algebraic Formula for Performance Bounds of a Weighted H_∞ Optimal Control Problem