Best Possible Region of Attraction for a Class of Unstable Systems Using Short Horizon MPC Concepts

This paper proposes a control strategy for input constrained second order systems with one unstable mode. For this class of systems, the largest region of attraction under bounded control is bounded in one direction whilst infinite in the other. Standard MPC type control with guaranteed stability either requires large control horizons or typically yields a much smaller region of attraction. We show that by extending MPC concepts a control strategy with a horizon of one is developed that provides asymptotic stability with the largest possible region of attraction under bounded control.