Set-based corral control in stochastic dynamical systems: Making almost invariant sets more invariant

Eric Forgoston, Lora Billings, Philip Yecko, Ira B. Schwartz

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

We consider the problem of stochastic prediction and control in a time-dependent stochastic environment, such as the ocean, where escape from an almost invariant region occurs due to random fluctuations. We determine high-probability control-actuation sets by computing regions of uncertainty, almost invariant sets, and Lagrangian coherent structures. The combination of geometric and probabilistic methods allows us to design regions of control, which provide an increase in loitering time while minimizing the amount of control actuation. We show how the loitering time in almost invariant sets scales exponentially with respect to the control actuation, causing an exponential increase in loitering times with only small changes in actuation force. The result is that the control actuation makes almost invariant sets more invariant.

Original languageEnglish
Article number013116
JournalChaos
Volume21
Issue number1
DOIs
StatePublished - 4 Feb 2011

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Stochastic Dynamical Systems
Invariant Set
dynamical systems
actuation
Dynamical systems
Invariant
Invariant Region
Control Sets
Coherent Structures
Probabilistic Methods
Ocean
escape
Fluctuations
oceans
Uncertainty
Computing
Prediction
predictions

Cite this

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abstract = "We consider the problem of stochastic prediction and control in a time-dependent stochastic environment, such as the ocean, where escape from an almost invariant region occurs due to random fluctuations. We determine high-probability control-actuation sets by computing regions of uncertainty, almost invariant sets, and Lagrangian coherent structures. The combination of geometric and probabilistic methods allows us to design regions of control, which provide an increase in loitering time while minimizing the amount of control actuation. We show how the loitering time in almost invariant sets scales exponentially with respect to the control actuation, causing an exponential increase in loitering times with only small changes in actuation force. The result is that the control actuation makes almost invariant sets more invariant.",
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Set-based corral control in stochastic dynamical systems : Making almost invariant sets more invariant. / Forgoston, Eric; Billings, Lora; Yecko, Philip; Schwartz, Ira B.

In: Chaos, Vol. 21, No. 1, 013116, 04.02.2011.

Research output: Contribution to journalArticle

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