Controlling chaos in a model of thermal pulse combustion

We describe methods for automating the control and tracking of states within or near a chaotic attractor. The methods are applied in a simulation using a recently developed model of thermal pulse combustion as the dynamical system. The controlled state is automatically tracked while a parameter is slowly changed well beyond the usual flame-out point where the chaotic attractor ceases to exist because of boundary crisis. A learning strategy based on simple neural networks is applied to map-based proportional feedback control algorithms both with and without a recursive term. Adaptive recursive proportional feedback is found to track farther beyond the crisis (flame-out) boundary than does the adaptive non-recursive map-based control. We also found that a continuous-time feedback proportional to the derivative of a system variable will stabilize and track an unstable fixed point near the chaotic attractor. The positive results suggest that a pulse combustor, and other nonlinear systems, may be suitably controlled to reduce undesirable cyclic variability and extend their useful operating range.