Floquet-based chaos control for continuous-time systems with stability analysis

In this Letter, a framework for controlling continuous-time chaotic systems is proposed. The framework is based on the Floquet theory of linear periodic differential equations and provides a practical method to stabilize unstable periodic orbits (UPOs) and a stability analysis of the closed loop systems. An example of controlling the circular restricted three-body problem known as halo orbits is illustrated. It is also reported that stabilization of UPOs can be effective by using the maximum principle to select a nominal orbit. It also turns out that the proposed framework enables us to give a theoretical account of the well-known occasional proportional feedback (OPF).