  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.
