Closed-loop control of a globally unstable jet using genetic programming*

When the density of a jet is sufficiently below that of its surroundings, it can become globally unstable, transitioning from a steady state to a self-excited state characterized by axisymmetric limit-cycle oscillations. We present experiments on the closed-loop control of such oscillations using an unsupervised data-driven model-free framework based on genetic programming (GP). Our implementation of this GP-based control framework relies on a hot-wire probe for sensing and a loudspeaker for actuation. We first initialize a generation of candidate control laws and evaluate their individual performance on the basis of a cost function that accounts for the amplitude of the global mode in a low-density jet and the actuation effort. We then breed further generations of control laws by enrolling them in a tournament and by executing genetic operations such as mutation, crossover, replication and elitism. By benchmarking the best GP-based control law against the best periodic forcing strategy found via conventional open-loop mapping, we show that GP-based control can provide a more efficient means of global mode suppression, offering new insight into the physics of hydrodynamically self-excited jets.