ON THE SUB-OPTIMAL FEEDBACK CONTROL LAW SYNTHESIS OF UNDERACTUATED SYSTEMS

In this paper, a complete solution on the suboptimal feedback control law synthesis for underactuated systems, based on the general optimization framework of the Dynamic Programming Theory is introduced. Control method proposed keeps the general structure of a suboptimal control approach, while the functional defining performance index is based on the underactuated system energy. Main application target of this contribution is on the electromechanical underactuated system stabilization about an unstable equilibrium point. This kind of system, has been stabilized by using two different control laws: the first one is used to swing up and the second one to balance around the unstable equilibrium point. Our main contribution is a single control synthesis methodology in order to swing up and asymptotically stabilize the underactuated system. In order to illustrate the application of the proposed technique, it is applied on two well-known systems: the Pendubot and the Rotatory Pendulum.