C.S. Daw, J.F. Thomas

Oak Ridge National Laboratory

Knoxville TN 37932-6472

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 a boundary crisis. A learning strategy based on simple neural networks is applied to map-based proportional feedback 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.

Rhode MA, Rollins RW, Markworth AJ, Edwards KD, Nguyen K, Daw CS, Thomas JF (1995). Controlling chaos in a model of thermal pulse combustion. Journal of Applied Physics

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