Controlling chaos using invariant manifolds

An analytic non-linear control method based on the concept of macrovariable control is proposed to stabilize chaotic systems. The system trajectory is attracted to some selected invariant manifold by continuous feedback of system states which can be used as perturbations on an available system parameter or outer-force control. A recursive design procedure is also developed to guarantee the asymptotic stability of the system with saturated small controlling signal. The method is applied to stabilizing two typical chaotic non-linear systems at some equilibrium or periodic orbit.