A Strategy for Chaos Control of Nonlinear Nonautonomous Systems

A general framework for local linear control of nonlinear nonautonomous systems using feedback strategies is considered. In particular, it is shown that a parametrically excited nonlinear system exhibiting chaos can be driven to a desired periodic motion or to a fixed point by designing a combination of a feed forward controller and a feedback time-periodic controller. The design of feedback controller can be achieved via two different techniques. In the first approach, the open-loop system is transformed to a time-invariant form through an application of Lyapunov-Floquet transformation. Then by constructing an auxiliary system , the feedback controller is designed in time -invariant domain by employing classical techniques, such as pole placement or optimal control. In the second approach, a symbolic technique is implemented to compute the Floquet transformation matrix (monodromy matrix) of the closed -loop system containing the unknown gain parameters of the controller. Then by using Jury’s criteria, the gain parameters can be selected to guarantee the orbital stability. Examples are presented to show engineering applications.