Control of chaotic and nonlinear systems influenced by dynamic noise

In this research, the effect of dynamic noise on OGY type control algorithms was studied. The research was done by conducting numerical experiments on a number of systems, i.e., the Hénon map, the Ikeda map, a model for internal combustion engines, and a model for continuous stirred tank reactors.

It was found that the fixed point location does not appear to be influenced by Gaussian noise. The manifold structure, however, does change with different noise intensities. Studies were also done to evaluate the effect of noise on directions of maximum and minimum contraction. These were found to be independent of Gaussian noise.

The original OGY control was found to be less that optimal when noise is added to the system. Comparisons were also made between the original OGY and a control algorithm based on the singular value decomposition. The SVD method appeared slightly more robust in noisy environments.

It was found that neither the original OGY, nor the SVD method were optimally suited for control when the system is being influenced by parametric noise. A number of guidelines were proposed and tested to optimize the search for the optimal control condition.