Exploiting Stochasticity for the Control of Transitions in Gyre Flows

Kularatne, Dhanushka; Forgoston, Eric; Hsieh, M. Ani

doi:10.15607/rss.2018.xiv.060

Cited by 3 publications

(1 citation statement)

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“…15 The required actuation for the strategy is minimal since the actual transition is precipitated by the noise in the system. We developed the approach in our previous work, 16 where we exploited noise-driven transitions to control the dwell time of a marine robot operating in a gyre ow. In this work, we generalize the approach to a broader class of dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

Using control to shape stochastic escape and switching dynamics

Kularatne

Forgoston

Hsieh

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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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 e ectiveness is numerically demonstrated for a set of dynamical systems of practical importance.Published under license by AIP Publishing. https://doi.Noise is an inherent phenomenon in all physical dynamical systems. Thus, the behavior of a dynamical system under the in uence of noise has been a widely studied topic. In particular, the e ect of small noise on the stability of a system has generated signi cant attention in the literature. It has been shown that under the in uence of noise, a system can be made to transition out of the its deterministically stable states. While these are rare occurences for small noise, they have a signi cant impact on the overall behavior of the system. The expected time for such a transition to occur, i.e., the mean switching time, is an important characteristic in such systems. In this work, we show how an external control could be used to enhance or abate this switching behavior and synthesize a feedback control strategy that actively changes the mean switching time to a desired value. This enables one to control the dwell time of the system in a given basin of attraction to a desired value. We analyze the controller using a representative one-dimensional system and demonstrate the controller on a set of dynamical systems with practical importance.Published under license by AIP Publishing. FIG. 3. The most probable switching path (MPSP) overlaid on the probability density of truncated escape trajectories obtained from Monte Carlo simulations of the double-gyre flow for parameters A = 1, s = 1, and µ = 1. The paths were truncated to highlight the escape portion of the trajectories.

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Section: Introductionmentioning

confidence: 99%