Nonlinear suboptimal control for a class of underactuated mechanical systems

This paper addresses to the problem of suboptimal control for a class of chained underactuated mechanical systems, whose dynamic linearization contains uncontrollable stable modes. In order to bring the system to its linearity domain and stabilize it without need of a switching control, a suboptimal control technique is proposed, based on the energy of the system and under the Bellman's Optimality Principle. A non-conventional, pendular-type underactuated dynamic system exhibiting particular features is studied to illustrate the presented approach; the swing-up and stabilization control of this numerical system about an unstable equilibrium point is shown.