Nonlinear feedback systems perturbed by noise: Steady-state probability distributions and optimal control

Daniel Liberzon; Roger W. Brockett

doi:10.1109/9.863596

Nonlinear feedback systems perturbed by noise: Steady-state probability distributions and optimal control

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

Abstract

In this paper we describe a class of nonlinear feedback systems perturbed by white noise for which explicit formulas for steady-state probability densities can be found. We show that this class includes what has been called monotemperaturic systems in earlier work and establish relationships with Lyapunov functions for the corresponding deterministic systems. We also treat a number of stochastic optimal control problems in the case of quantized feedback, with performance criteria formulated in terms of the steady-state probability density.

Original language	English (US)
Pages (from-to)	1116-1130
Number of pages	15
Journal	IEEE Transactions on Automatic Control
Volume	45
Issue number	6
DOIs	https://doi.org/10.1109/9.863596
State	Published - Jun 2000
Externally published	Yes

Keywords

Nonlinear feedback system
Quantizer
Steady-state probability density
Stochastic optimal control
White noise

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

Online availability

10.1109/9.863596

Library availability

Discover UIUC Full Text

Cite this

@article{718e60d17f864870a10ce11d9687ba51,

title = "Nonlinear feedback systems perturbed by noise: Steady-state probability distributions and optimal control",

abstract = "In this paper we describe a class of nonlinear feedback systems perturbed by white noise for which explicit formulas for steady-state probability densities can be found. We show that this class includes what has been called monotemperaturic systems in earlier work and establish relationships with Lyapunov functions for the corresponding deterministic systems. We also treat a number of stochastic optimal control problems in the case of quantized feedback, with performance criteria formulated in terms of the steady-state probability density.",

keywords = "Nonlinear feedback system, Quantizer, Steady-state probability density, Stochastic optimal control, White noise",

author = "Daniel Liberzon and Brockett, {Roger W.}",

note = "Funding Information: Manuscript received March 20, 1998; revised April 30, 1999. Recommended by Associate Editor, Q. Zhang. The work of D. Liberzon was supported in part by ARO DAAH04-95-1-0114, NSF ECS 9634146, and AFOSR F49620-97-1-0108. The work of R. W. Brockett was supported in part by the U. S. Army under Contracts DAAH 04-96-1-0445, DAAG 55-97-1-0114, and DAAL 03-92-G-0115.",

year = "2000",

month = jun,

doi = "10.1109/9.863596",

language = "English (US)",

volume = "45",

pages = "1116--1130",

journal = "IRE Transactions on Automatic Control",

issn = "0018-9286",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "6",

}

TY - JOUR

T1 - Nonlinear feedback systems perturbed by noise

T2 - Steady-state probability distributions and optimal control

AU - Liberzon, Daniel

AU - Brockett, Roger W.

N1 - Funding Information: Manuscript received March 20, 1998; revised April 30, 1999. Recommended by Associate Editor, Q. Zhang. The work of D. Liberzon was supported in part by ARO DAAH04-95-1-0114, NSF ECS 9634146, and AFOSR F49620-97-1-0108. The work of R. W. Brockett was supported in part by the U. S. Army under Contracts DAAH 04-96-1-0445, DAAG 55-97-1-0114, and DAAL 03-92-G-0115.

PY - 2000/6

Y1 - 2000/6

N2 - In this paper we describe a class of nonlinear feedback systems perturbed by white noise for which explicit formulas for steady-state probability densities can be found. We show that this class includes what has been called monotemperaturic systems in earlier work and establish relationships with Lyapunov functions for the corresponding deterministic systems. We also treat a number of stochastic optimal control problems in the case of quantized feedback, with performance criteria formulated in terms of the steady-state probability density.

AB - In this paper we describe a class of nonlinear feedback systems perturbed by white noise for which explicit formulas for steady-state probability densities can be found. We show that this class includes what has been called monotemperaturic systems in earlier work and establish relationships with Lyapunov functions for the corresponding deterministic systems. We also treat a number of stochastic optimal control problems in the case of quantized feedback, with performance criteria formulated in terms of the steady-state probability density.

KW - Nonlinear feedback system

KW - Quantizer

KW - Steady-state probability density

KW - Stochastic optimal control

KW - White noise

UR - http://www.scopus.com/inward/record.url?scp=0034195810&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034195810&partnerID=8YFLogxK

U2 - 10.1109/9.863596

DO - 10.1109/9.863596

M3 - Article

AN - SCOPUS:0034195810

SN - 0018-9286

VL - 45

SP - 1116

EP - 1130

JO - IRE Transactions on Automatic Control

JF - IRE Transactions on Automatic Control

IS - 6

ER -

Nonlinear feedback systems perturbed by noise: Steady-state probability distributions and optimal control

Abstract

Keywords

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this