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We present here a new approach of the partial control method, which is auseful control technique applied to transient chaotic dynamics affected by abounded noise. Usually we want to avoid the escape of these chaotic transientsoutside a certain region $Q$ of the phase space. For that purpose, there existsa control bound such that for controls smaller than this bound trajectories arekept in a special subset of $Q$ called the safe set. The aim of this newapproach is to go further, and to compute for every point of $Q$ the minimalcontrol bound that would keep it in $Q$. This defines a special function thatwe call the safety function, which can provide the necessary information tocompute the safe set once we choose a particular value of the control bound.This offers a generalized method where previous known cases are included, andits use encompasses more diverse scenarios.

A new approach of the partial control method in chaotic systems