  Model predictive control (MPC) has been used successfully in diverse
applications. As its name suggests, MPC requires a model for predictive
optimization. The present paper focuses on the application of MPC to a Rijke
tube, in which a heating source and acoustic dynamics interact to produce
self-excited oscillations. Since the dynamics of a Rijke tube are difficult to
model to a high level of accuracy, the implementation of MPC requires
leveraging data from the physical setup as well as knowledge about
thermoacoustics, which is labor intensive and requires domain expertise. With
this motivation, the present paper uses predictive cost adaptive control (PCAC)
for sampled-data control of an experimental Rijke-tube setup. PCAC performs
online closed-loop linear model identification for receding-horizon
optimization based on the backward propagating Riccati equation. In place of
analytical modeling, open-loop experiments are used to create a simple
emulation model, which is used for choosing PCAC hyperparameters. PCAC is
applied to the Rijke-tube setup under various experimental scenarios.
