Using control to shape stochastic escape and switching dynamics

Dhanushka Kularatne, Eric Forgoston, M. Ani Hsieh

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We present a strategy to control the mean stochastic switching times of general dynamical systems with multiple equilibrium states subject to Gaussian white noise. The control can either enhance or abate the probability of escape from the deterministic region of attraction of a stable equilibrium in the presence of external noise. We synthesize a feedback control strategy that actively changes the system's mean stochastic switching behavior based on the system's distance to the boundary of the attracting region. With the proposed controller, we are able to achieve a desired mean switching time, even when the strength of noise in the system is not known. The control method is analytically validated using a one-dimensional system, and its effectiveness is numerically demonstrated for a set of dynamical systems of practical importance.

Original languageEnglish
Article number053128
JournalChaos
Volume29
Issue number5
DOIs
StatePublished - 1 May 2019

Fingerprint

escape
dynamical systems
Dynamical systems
Dynamical system
Multiple Equilibria
One-dimensional System
Gaussian White Noise
White noise
white noise
feedback control
Equilibrium State
Feedback Control
Feedback control
attraction
Control Strategy
controllers
Controller
Controllers
Strategy

Cite this

Kularatne, Dhanushka ; Forgoston, Eric ; Hsieh, M. Ani. / Using control to shape stochastic escape and switching dynamics. In: Chaos. 2019 ; Vol. 29, No. 5.
@article{fa1449b123224280a951362dc60922be,
title = "Using control to shape stochastic escape and switching dynamics",
abstract = "We present a strategy to control the mean stochastic switching times of general dynamical systems with multiple equilibrium states subject to Gaussian white noise. The control can either enhance or abate the probability of escape from the deterministic region of attraction of a stable equilibrium in the presence of external noise. We synthesize a feedback control strategy that actively changes the system's mean stochastic switching behavior based on the system's distance to the boundary of the attracting region. With the proposed controller, we are able to achieve a desired mean switching time, even when the strength of noise in the system is not known. The control method is analytically validated using a one-dimensional system, and its effectiveness is numerically demonstrated for a set of dynamical systems of practical importance.",
author = "Dhanushka Kularatne and Eric Forgoston and Hsieh, {M. Ani}",
year = "2019",
month = "5",
day = "1",
doi = "10.1063/1.5090113",
language = "English",
volume = "29",
journal = "Chaos",
issn = "1054-1500",
publisher = "American Institute of Physics",
number = "5",

}

Using control to shape stochastic escape and switching dynamics. / Kularatne, Dhanushka; Forgoston, Eric; Hsieh, M. Ani.

In: Chaos, Vol. 29, No. 5, 053128, 01.05.2019.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Using control to shape stochastic escape and switching dynamics

AU - Kularatne, Dhanushka

AU - Forgoston, Eric

AU - Hsieh, M. Ani

PY - 2019/5/1

Y1 - 2019/5/1

N2 - We present a strategy to control the mean stochastic switching times of general dynamical systems with multiple equilibrium states subject to Gaussian white noise. The control can either enhance or abate the probability of escape from the deterministic region of attraction of a stable equilibrium in the presence of external noise. We synthesize a feedback control strategy that actively changes the system's mean stochastic switching behavior based on the system's distance to the boundary of the attracting region. With the proposed controller, we are able to achieve a desired mean switching time, even when the strength of noise in the system is not known. The control method is analytically validated using a one-dimensional system, and its effectiveness is numerically demonstrated for a set of dynamical systems of practical importance.

AB - We present a strategy to control the mean stochastic switching times of general dynamical systems with multiple equilibrium states subject to Gaussian white noise. The control can either enhance or abate the probability of escape from the deterministic region of attraction of a stable equilibrium in the presence of external noise. We synthesize a feedback control strategy that actively changes the system's mean stochastic switching behavior based on the system's distance to the boundary of the attracting region. With the proposed controller, we are able to achieve a desired mean switching time, even when the strength of noise in the system is not known. The control method is analytically validated using a one-dimensional system, and its effectiveness is numerically demonstrated for a set of dynamical systems of practical importance.

UR - http://www.scopus.com/inward/record.url?scp=85066784044&partnerID=8YFLogxK

U2 - 10.1063/1.5090113

DO - 10.1063/1.5090113

M3 - Article

VL - 29

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 5

M1 - 053128

ER -