Enlarging the region of attraction for underactuated systems using impulsive inputs

Underactuated systems typically have multiple equilibria and therefore a stabilizing controller is effective for initial configurations that lie within the region of attraction of the equilibrium. An impulsive control algorithm is proposed to enlarge this region of attraction of the stabilized equilibrium. The algorithm uses impulsive inputs that are applied in conjunction with the stabilizing controller, and the success of the algorithm depends on two sufficient conditions that need to be satisfied. The algorithm is applied to the Pendubot and the Acrobot and numerical simulation results establish its effectiveness.