A simple adaptive-feedback controller for high-quality chaos synchronization

Based on the invariance principle of differential equations, a simple adaptive-feedback scheme is proposed to strictly synchronize almost all chaotic systems. Unlike the usual linear feedback, the variable feedback strength is automatically adapted to completely synchronize two almost arbitrary identical chaotic systems, so this scheme is analytical, and simple to implement in practice. Moreover it is quite robust against the effect of noise. The famous Lorenz and R$\ddot{\textrm{o}}$ssler hyperchaos systems are used as illustrative examples.