Modified energy-balancing-based control for the tracking problem

The authors extend energy-balancing-based control for set-point regulation to the problem of trajectory tracking for Euler-Lagrange (EL) systems. In addition to producing a new tracking control, this method also provides a re-interpretation of established results, such as computed torque control, PD+ control and Slotine-Li control. The authors also consider port-controlled Hamiltonian (PCH) systems, which are more general than EL systems. They develop a new matching equation for PCH systems so that interconnection damping assignment passivity-based control (IDA-PBC) can be applied to the control of a larger class of under-actuated PCH systems and the tracking control of some non-passive systems.