# Closed-loop adaptive control of extreme events in a turbulent flow

## TL;DR

This paper presents a novel adaptive control strategy that predicts and mitigates extreme events in turbulent flows with minimal disturbance, maintaining the system's core chaotic behavior.

## Contribution

The authors introduce a probabilistic prediction-based control method that targets only the degrees of freedom involved in extreme events, preserving the system's natural dynamics.

## Key findings

- Effective mitigation of extreme events in turbulent shear flow
- Controlled system retains chaotic core similar to uncontrolled system
- Minimal interference achieved by targeting specific flow degrees of freedom

## Abstract

Extreme events that arise spontaneously in chaotic dynamical systems often have an adverse impact on the system or the surrounding environment. As such, their mitigation is highly desirable. Here, we introduce a novel control strategy for mitigating extreme events in a turbulent shear flow. The controller combines a probabilistic prediction of the extreme events with a deterministic actuator. The predictions are used to actuate the controller only when an extreme event is imminent. When actuated, the controller only acts on the degrees of freedom that are involved in the formation of the extreme events, exerting minimal interference with the flow dynamics. As a result, the attractors of the controlled and uncontrolled systems share the same chaotic core (containing the non-extreme events) and only differ in the tail of their distributions. We propose that such adaptive low-dimensional controllers should be used to mitigate extreme events in general chaotic dynamical systems, beyond the shear flow considered here.