On global external stochastic stabilization of linear systems with input saturation

Antonie Arij Stoorvogel; Ali Saberi

doi:10.1109/ACC.2015.7170827

On global external stochastic stabilization of linear systems with input saturation

Antonie Arij Stoorvogel, Ali Saberi

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

We consider the problem of global external stochastic stabilization for linear plants with saturating actuators, driven by a stochastic external disturbance, and having random Gaussian-distributed initial conditions. The aim of this stabilization is to control such plants by a possibly nonlinear static state feedback law that achieves global asymptotic stability in the absence of disturbances, while guaranteeing a bounded variance of the state vector for all time in the presence of disturbances and Gaussian distributed initial conditions. Results for continuous-time open-loop critically stable plants have been obtained before. The goal of this paper is to extend this result to critically unstable plants. We view our contribution in this paper as a first critical step in solving the LQG control problem for linear systems subject to saturated inputs which is a research problem with a long history in our field.

Original language	Undefined
Title of host publication	American Control Conference, ACC 2015
Place of Publication	Piscataway, NJ, USA
Publisher	IEEE
Pages	769-774
Number of pages	6
ISBN (Print)	978-1-4799-8686-6
DOIs	https://doi.org/10.1109/ACC.2015.7170827
Publication status	Published - 1 Jul 2015
Event	2015 American Control Conference, ACC 2015 - Chicago, United States Duration: 1 Jul 2015 → 3 Jul 2015

Publication series

Name
Publisher	IEEE

Conference

Conference	2015 American Control Conference, ACC 2015
Abbreviated title	ACC
Country/Territory	United States
City	Chicago
Period	1/07/15 → 3/07/15

Keywords

EWI-26614
METIS-315610
IR-99223

Access to Document

10.1109/ACC.2015.7170827

http://eprints.eemcs.utwente.nl/secure2/26614/01/p134.pdf

Cite this

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title = "On global external stochastic stabilization of linear systems with input saturation",

abstract = "We consider the problem of global external stochastic stabilization for linear plants with saturating actuators, driven by a stochastic external disturbance, and having random Gaussian-distributed initial conditions. The aim of this stabilization is to control such plants by a possibly nonlinear static state feedback law that achieves global asymptotic stability in the absence of disturbances, while guaranteeing a bounded variance of the state vector for all time in the presence of disturbances and Gaussian distributed initial conditions. Results for continuous-time open-loop critically stable plants have been obtained before. The goal of this paper is to extend this result to critically unstable plants. We view our contribution in this paper as a first critical step in solving the LQG control problem for linear systems subject to saturated inputs which is a research problem with a long history in our field.",

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author = "Stoorvogel, {Antonie Arij} and Ali Saberi",

note = "10.1109/ACC.2015.7170827 ; 2015 American Control Conference, ACC 2015 ; Conference date: 01-07-2015 Through 03-07-2015",

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doi = "10.1109/ACC.2015.7170827",

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T1 - On global external stochastic stabilization of linear systems with input saturation

AU - Stoorvogel, Antonie Arij

AU - Saberi, Ali

N1 - 10.1109/ACC.2015.7170827

PY - 2015/7/1

Y1 - 2015/7/1

N2 - We consider the problem of global external stochastic stabilization for linear plants with saturating actuators, driven by a stochastic external disturbance, and having random Gaussian-distributed initial conditions. The aim of this stabilization is to control such plants by a possibly nonlinear static state feedback law that achieves global asymptotic stability in the absence of disturbances, while guaranteeing a bounded variance of the state vector for all time in the presence of disturbances and Gaussian distributed initial conditions. Results for continuous-time open-loop critically stable plants have been obtained before. The goal of this paper is to extend this result to critically unstable plants. We view our contribution in this paper as a first critical step in solving the LQG control problem for linear systems subject to saturated inputs which is a research problem with a long history in our field.

AB - We consider the problem of global external stochastic stabilization for linear plants with saturating actuators, driven by a stochastic external disturbance, and having random Gaussian-distributed initial conditions. The aim of this stabilization is to control such plants by a possibly nonlinear static state feedback law that achieves global asymptotic stability in the absence of disturbances, while guaranteeing a bounded variance of the state vector for all time in the presence of disturbances and Gaussian distributed initial conditions. Results for continuous-time open-loop critically stable plants have been obtained before. The goal of this paper is to extend this result to critically unstable plants. We view our contribution in this paper as a first critical step in solving the LQG control problem for linear systems subject to saturated inputs which is a research problem with a long history in our field.

KW - EWI-26614

KW - METIS-315610

KW - IR-99223

U2 - 10.1109/ACC.2015.7170827

DO - 10.1109/ACC.2015.7170827

M3 - Conference contribution

SN - 978-1-4799-8686-6

SP - 769

EP - 774

BT - American Control Conference, ACC 2015

PB - IEEE

CY - Piscataway, NJ, USA

T2 - 2015 American Control Conference, ACC 2015

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