On passivity based control for partial stabilization of underactuated systems

The stabilization problem for a class of underactuated Lagrangian systems with respect to part of the state variables is considered. It is assumed that this part of the state variables is directly affected by control. Moreover, on the rest of the variables we impose additional constraints, based on the form of the total energy of the system, which should be valid after the transition time. Intuitively this can be interpreted as a decoupling, by the suggested control strategy, of the state variables into parts. To motivate this investigation, the problem of swinging the Pendubot is considered