The flow dynamics, resulting from the interaction between a boundary layer and a wall cavity open to the main flow, can be adjusted to obtain more or less pronounced nonlinear interactions between the instability modes of the resonant mixing layer and intracavity spanwise centrifugal instabilities [1]. This configuration provides a particularly challenging benchmark for testing the effectiveness of control procedures in fluid systems. With the aim of suppressing cavity resonance, we propose a closed-loop control experiment whose controller results from an automatic learning procedure based on a genetic programming algorithm enhanced with a gradient method (gMLC) (gMLC) [2].