Neural network-based backstepping design for the synchronization of cross-strict feedback hyperchaotic systems with unmatched uncertainties

Abstract

For a class of cross-strict feedback hyperchaotic systems with unmatched uncertainties, a multilayer neural network (MNN) based adaptive backstepping design method is proposed. An MNN is introduced to estimate the uncertainties in systems. Sliding mode and adaptive backstepping control are used to deal with the unmatched uncertainties and the MNN approximation errors. If the virtual control coefficients do not pass through zeros, the proposed method guarantees that the synchronization errors of the systems approach zeros. If the virtual control coefficients pass through zeros, the proposed method guarantees that the synchronization errors of the systems are bounded. Numerical simulations are given to demonstrate the efficiency of the proposed control scheme.