Cluster-based control of self-excited thermoacoustic oscillations in a Rijke tube

We apply a cluster-based control strategy to a Rijke tube model to weaken its self-excited thermoacoustic oscillations. Specifically, we partition the pressure and heat-release-rate fluctuations of the system into discrete clusters within a low-dimensional feature space. We then identify the optimal feedback control laws via a Nelder--Mead simplex search applied to a cost function that balances the reduction in thermoacoustic amplitude with the actuation cost. We demonstrate that this data-driven control strategy can suppress a variety of self-excited thermoacoustic oscillations with minimal actuation cost, even in the presence of strong measurement noise and time delays in the control loop. Overall, this approach shows promise for improving the stability and performance of thermoacoustic systems, opening up potential applications in fields such as energy conversion and combustion.