L1 adaptive control for positive LTI systems

Hui Sun; Quanyan Zhu; Naira Hovakimyan; Tamer Başar

L₁ adaptive control for positive LTI systems

Hui Sun, Quanyan Zhu, Naira Hovakimyan, Tamer Başar

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Positive systems represent a class of systems whose state variables are nonnegative. This paper presents an L₁ adaptive controller for such systems. The control objective is to force the system output track a given nonnegative reference signal. In the analysis of the L₁ adaptive controller, we first show the positivity of the constructed reference system, and then demonstrate that the controlled system states track those of the reference system. We provide the uniform transient and steady-state performance bounds on the system state and the control signals, which can be systematically improved by increasing the adaptation rate, under the assumption that the unknown system parameters are positive. Simulations are presented to corroborate our results.

Original language	English (US)
Title of host publication	Proceedings of the 2011 American Control Conference, ACC 2011
Pages	13-18
Number of pages	6
State	Published - 2011
Event	2011 American Control Conference, ACC 2011 - San Francisco, CA, United States Duration: Jun 29 2011 → Jul 1 2011

Publication series

Name	Proceedings of the American Control Conference
ISSN (Print)	0743-1619

Other

Other	2011 American Control Conference, ACC 2011
Country/Territory	United States
City	San Francisco, CA
Period	6/29/11 → 7/1/11

ASJC Scopus subject areas

Electrical and Electronic Engineering

Cite this

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title = "L1 adaptive control for positive LTI systems",

abstract = "Positive systems represent a class of systems whose state variables are nonnegative. This paper presents an L1 adaptive controller for such systems. The control objective is to force the system output track a given nonnegative reference signal. In the analysis of the L1 adaptive controller, we first show the positivity of the constructed reference system, and then demonstrate that the controlled system states track those of the reference system. We provide the uniform transient and steady-state performance bounds on the system state and the control signals, which can be systematically improved by increasing the adaptation rate, under the assumption that the unknown system parameters are positive. Simulations are presented to corroborate our results.",

author = "Hui Sun and Quanyan Zhu and Naira Hovakimyan and Tamer Ba{\c s}ar",

year = "2011",

language = "English (US)",

isbn = "9781457700804",

series = "Proceedings of the American Control Conference",

pages = "13--18",

booktitle = "Proceedings of the 2011 American Control Conference, ACC 2011",

note = "2011 American Control Conference, ACC 2011 ; Conference date: 29-06-2011 Through 01-07-2011",

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AU - Sun, Hui

AU - Zhu, Quanyan

AU - Hovakimyan, Naira

AU - Başar, Tamer

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N2 - Positive systems represent a class of systems whose state variables are nonnegative. This paper presents an L1 adaptive controller for such systems. The control objective is to force the system output track a given nonnegative reference signal. In the analysis of the L1 adaptive controller, we first show the positivity of the constructed reference system, and then demonstrate that the controlled system states track those of the reference system. We provide the uniform transient and steady-state performance bounds on the system state and the control signals, which can be systematically improved by increasing the adaptation rate, under the assumption that the unknown system parameters are positive. Simulations are presented to corroborate our results.

AB - Positive systems represent a class of systems whose state variables are nonnegative. This paper presents an L1 adaptive controller for such systems. The control objective is to force the system output track a given nonnegative reference signal. In the analysis of the L1 adaptive controller, we first show the positivity of the constructed reference system, and then demonstrate that the controlled system states track those of the reference system. We provide the uniform transient and steady-state performance bounds on the system state and the control signals, which can be systematically improved by increasing the adaptation rate, under the assumption that the unknown system parameters are positive. Simulations are presented to corroborate our results.

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T3 - Proceedings of the American Control Conference

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BT - Proceedings of the 2011 American Control Conference, ACC 2011

T2 - 2011 American Control Conference, ACC 2011

Y2 - 29 June 2011 through 1 July 2011

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