An intelligent control of chaos in Lorenz system with a dynamic wavelet network

Abstract

This paper proposes a dynamic wavelet network based intelligent adaptive controller design to regulate the chaotic states of the Lorenz equations. The “Dynamic Wavelet Network (DWN)” has lag dynamics, non-orthogonal mother wavelets as activation function and interconnection weights. Adaptation is done by adjusting parameters of the DWN to minimize the cost functional of the Lorenz system operating state errors. The cost gradients with respect to the network parameters are calculated by adjoint sensitivity analysis. It is illustrated in simulations that this control approach is more successful than the previous controllers for eliminating the tracking errors due to the set point changes.