Optimal targeting in chaos control: A discrete Hamiltonian approach

One of the most interesting paradigms of chaos control is the possibility of switching a system between different unstable periodic orbits (UPOs) with effectively zero control energy. We give a robust method to find finite-time optimal transient trajectories, and show how to stabilize both, UPOs and transients, within the same LQ-framework. The method is quite general, and can also be used to drive a system from static stationary points to an UPO. To illustrate our approach we apply it to the controlled logistic map, and also to an experimental driven-pendulum setup.