Control of single-degree-of-freedom Hamiltonian systems with impulsive inputs

This paper develops a theory for the feedback control of single degree-of-freedom Hamiltonian systems, utilizing inputs which approximate delta-functions. The main idea is that by using ''spikey'' control inputs, it is possible to force the system to jump between energy levels. Since there is a correspondence between energy levels and orbits for Hamiltonian systems, this control of system energy results in control of the system dynamics. Impulsive control has proven useful in simulations and experiments involving the global reconfiguration of mechanical systems. We present application of the control to the cart, and pendulum swing-up problem.