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

TL;DR

This paper introduces a control strategy for stochastic dynamical systems that enhances the invariance of almost invariant sets, thereby increasing the time systems remain within desired regions despite random fluctuations.

Contribution

It combines geometric and probabilistic methods to design control regions that significantly extend loitering times with minimal actuation in stochastic environments.

Findings

Loitering time scales exponentially with control actuation.

Control actuation effectively makes almost invariant sets more invariant.

Method reduces control effort needed to maintain system within desired regions.

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 that 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.