Event-triggered control of nonlinear systems: A small-gain approach

Tengfei Liu, Zhong-Ping Jiang

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This chapter studies the event-triggered control problem for nonlinear systems with input-to-state stability (ISS) as the basic notion and the ISS small-gain theorem as a tool. The contribution of this book chapter is twofold. First, an ISS gain condition is proposed for event-triggered control of nonlinear uncertain systems. It is proved that infinitely fast sampling can be avoided with an appropriately designed event-triggering mechanism if the system is input-to-state stabilizable with measurement error as the external input and the resulted ISS gain is Lipschitz on compact sets. No assumption on the existence of known ISS-Lyapunov functions is made in the discussions. Moreover, the forward completeness problem with event-triggered control is studied systematically by ISS small-gain arguments. Self-triggered control designs for systems under external disturbance are also developed in the ISS-based framework. Second, this chapter introduces a new design method for input-to-state stabilization of nonlinear uncertain systems in the strict-feedback form. It is particularly shown that the ISS gain with the measurement error as the input can be designed to satisfy the proposed condition for event-triggered control.

Original languageEnglish (US)
Title of host publicationLecture Notes in Control and Information Sciences
PublisherSpringer Verlag
Pages53-97
Number of pages45
Volume473
DOIs
StatePublished - Mar 1 2017

Publication series

NameLecture Notes in Control and Information Sciences
Volume473
ISSN (Print)01708643

Fingerprint

event
self-control
stabilization

ASJC Scopus subject areas

  • Library and Information Sciences

Cite this

Liu, T., & Jiang, Z-P. (2017). Event-triggered control of nonlinear systems: A small-gain approach. In Lecture Notes in Control and Information Sciences (Vol. 473, pp. 53-97). (Lecture Notes in Control and Information Sciences; Vol. 473). Springer Verlag. https://doi.org/10.1007/978-3-319-51298-3_3

Event-triggered control of nonlinear systems : A small-gain approach. / Liu, Tengfei; Jiang, Zhong-Ping.

Lecture Notes in Control and Information Sciences. Vol. 473 Springer Verlag, 2017. p. 53-97 (Lecture Notes in Control and Information Sciences; Vol. 473).

Research output: Chapter in Book/Report/Conference proceedingChapter

Liu, T & Jiang, Z-P 2017, Event-triggered control of nonlinear systems: A small-gain approach. in Lecture Notes in Control and Information Sciences. vol. 473, Lecture Notes in Control and Information Sciences, vol. 473, Springer Verlag, pp. 53-97. https://doi.org/10.1007/978-3-319-51298-3_3
Liu T, Jiang Z-P. Event-triggered control of nonlinear systems: A small-gain approach. In Lecture Notes in Control and Information Sciences. Vol. 473. Springer Verlag. 2017. p. 53-97. (Lecture Notes in Control and Information Sciences). https://doi.org/10.1007/978-3-319-51298-3_3
Liu, Tengfei ; Jiang, Zhong-Ping. / Event-triggered control of nonlinear systems : A small-gain approach. Lecture Notes in Control and Information Sciences. Vol. 473 Springer Verlag, 2017. pp. 53-97 (Lecture Notes in Control and Information Sciences).
@inbook{709b5bc0a5c6406e8ce8c71329824261,
title = "Event-triggered control of nonlinear systems: A small-gain approach",
abstract = "This chapter studies the event-triggered control problem for nonlinear systems with input-to-state stability (ISS) as the basic notion and the ISS small-gain theorem as a tool. The contribution of this book chapter is twofold. First, an ISS gain condition is proposed for event-triggered control of nonlinear uncertain systems. It is proved that infinitely fast sampling can be avoided with an appropriately designed event-triggering mechanism if the system is input-to-state stabilizable with measurement error as the external input and the resulted ISS gain is Lipschitz on compact sets. No assumption on the existence of known ISS-Lyapunov functions is made in the discussions. Moreover, the forward completeness problem with event-triggered control is studied systematically by ISS small-gain arguments. Self-triggered control designs for systems under external disturbance are also developed in the ISS-based framework. Second, this chapter introduces a new design method for input-to-state stabilization of nonlinear uncertain systems in the strict-feedback form. It is particularly shown that the ISS gain with the measurement error as the input can be designed to satisfy the proposed condition for event-triggered control.",
author = "Tengfei Liu and Zhong-Ping Jiang",
year = "2017",
month = "3",
day = "1",
doi = "10.1007/978-3-319-51298-3_3",
language = "English (US)",
volume = "473",
series = "Lecture Notes in Control and Information Sciences",
publisher = "Springer Verlag",
pages = "53--97",
booktitle = "Lecture Notes in Control and Information Sciences",
address = "Germany",

}

TY - CHAP

T1 - Event-triggered control of nonlinear systems

T2 - A small-gain approach

AU - Liu, Tengfei

AU - Jiang, Zhong-Ping

PY - 2017/3/1

Y1 - 2017/3/1

N2 - This chapter studies the event-triggered control problem for nonlinear systems with input-to-state stability (ISS) as the basic notion and the ISS small-gain theorem as a tool. The contribution of this book chapter is twofold. First, an ISS gain condition is proposed for event-triggered control of nonlinear uncertain systems. It is proved that infinitely fast sampling can be avoided with an appropriately designed event-triggering mechanism if the system is input-to-state stabilizable with measurement error as the external input and the resulted ISS gain is Lipschitz on compact sets. No assumption on the existence of known ISS-Lyapunov functions is made in the discussions. Moreover, the forward completeness problem with event-triggered control is studied systematically by ISS small-gain arguments. Self-triggered control designs for systems under external disturbance are also developed in the ISS-based framework. Second, this chapter introduces a new design method for input-to-state stabilization of nonlinear uncertain systems in the strict-feedback form. It is particularly shown that the ISS gain with the measurement error as the input can be designed to satisfy the proposed condition for event-triggered control.

AB - This chapter studies the event-triggered control problem for nonlinear systems with input-to-state stability (ISS) as the basic notion and the ISS small-gain theorem as a tool. The contribution of this book chapter is twofold. First, an ISS gain condition is proposed for event-triggered control of nonlinear uncertain systems. It is proved that infinitely fast sampling can be avoided with an appropriately designed event-triggering mechanism if the system is input-to-state stabilizable with measurement error as the external input and the resulted ISS gain is Lipschitz on compact sets. No assumption on the existence of known ISS-Lyapunov functions is made in the discussions. Moreover, the forward completeness problem with event-triggered control is studied systematically by ISS small-gain arguments. Self-triggered control designs for systems under external disturbance are also developed in the ISS-based framework. Second, this chapter introduces a new design method for input-to-state stabilization of nonlinear uncertain systems in the strict-feedback form. It is particularly shown that the ISS gain with the measurement error as the input can be designed to satisfy the proposed condition for event-triggered control.

UR - http://www.scopus.com/inward/record.url?scp=85017008260&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85017008260&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-51298-3_3

DO - 10.1007/978-3-319-51298-3_3

M3 - Chapter

VL - 473

T3 - Lecture Notes in Control and Information Sciences

SP - 53

EP - 97

BT - Lecture Notes in Control and Information Sciences

PB - Springer Verlag

ER -