Supervising a Family of Hybrid Controllers for Robust Global Asymptotic Stabilization

This paper describes an algorithm for achieving robust, global asymptotic stabilization in nonlinear control systems by supervising the actions of a family of hybrid controllers. The family is such that the regions over which they operate cover the state space in an appropriate sense. Moreover, their behavior is such that they can be scheduled to move the state of the system toward a desirable region, whether it be an equilibrium point or a compact set. In establishing our main result, we use the concept of "events" for hybrid systems and show that, under mild assumptions, stability of a system without events is preserved when a finite number of events are incorporated. The algorithm is applied to robust, global stabilization problems involving vehicle orientation, position and orientation of a mobile robot, and the inverted configuration of a pendulum.