Genetic programming control of quasiperiodic and chaotic oscillations in a thermoacoustic system

Self-excited thermoacoustic oscillations remain a key obstacle to low-emission combustion, especially in time-aperiodic regimes where quasiperiodic and chaotic dynamics hinder conventional controller design. We experimentally demonstrate data-driven suppression of such aperiodic thermoacoustic oscillations in a flame-driven Rijke tube using genetic programming (GP). In closed-loop form, the GP-discovered control laws are static nonlinear feedback maps that generate, in real time, actuation commands from a sensor signal. Performance is evaluated by a cost function that penalises both the thermoacoustic amplitude (state cost) and the actuation effort (input cost), enabling efficiency comparisons. We benchmark GP closed-loop control (GCC) against GP open-loop control and conventional open-loop harmonic forcing. In the quasiperiodic regime, all three strategies achieve nearly 90 percent sign 90 % $90\,%$ amplitude reduction, but the closed-loop strategy is the most efficient. The low-amplitude controlled state is dominated by a preferred (high-gain) mode of the open-flame describing function, and can persist even after control deactivation, indicating basin-of-attraction switching. In the chaotic regime, GCC again outperforms both open-loop strategies, achieving the largest thermoacoustic amplitude reduction with minimal actuation effort. Synchronisation analysis reveals phase trapping, drifting and locking between pressure and heat-release-rate fluctuations, while the 0–1 test and complexity–entropy diagnostics reveal that the GP-suppressed state retains measurable signatures of deterministic chaos. Overall, this study shows that GP control can provide an efficient model-free tool for suppressing aperiodic thermoacoustic oscillations by autonomously exploiting high-receptivity flame pathways with state-dependent actuation.