Estimation of the Region of Attraction of Underactuated Systems and Its Enlargement Using Impulsive Inputs

Stabilization of an equilibrium point is an important control problem for underactuated systems. For a given control design, the ability of the system to remain stable in the presence of disturbances depends on the size of the region of attraction of the stabilized equilibrium. The sum of squares and trajectory reversing methods are combined together to generate a large estimate of the region of attraction. Then, this estimate is effectively enlarged by applying the impulse manifold method, which can stabilize equilibria from points lying outside the estimated region of attraction. In this paper, the generality of the approach is demonstrated using simulations of a three-link underactuated system. Experimental validation using the pendubot is provided to demonstrate the feasibility of practical implementation.