Active control of nonlinear systems exhibiting chaos

A general framework for the local control of chaos in non-autonomous systems using feedback strategies is considered. It is shown that a system exhibiting chaos can be driven to a desired periodic motion by designing a combination of feedforward controller and a time-varying controller. The design of the time-varying controller is achieved through an application of Liapunov-Floquet transformation which guarantees the local stability of the desired periodic orbit. The chaotic motion may alternately be driven to a fixed point by replacing the time-varying controller with a constant gain controller, which may be designed using classical techniques, viz., pole placement, etc. A sinusoidally driven Duffing´s oscillator is chosen as an illustrative example to demonstrate the application