  Control of a hybrid dynamical system can manifest in one of two main ways:
either through the continuous or the discrete dynamics. An example of controls
influencing the continuous dynamics is legged locomotion, where the joints are
actuated but the location and nature of the impacts are uncontrolled. In
contrast, an example of discrete control would be in tennis; the player can
only influence the trajectory of the ball through striking it.
  This work examines the latter case with two key emphases. The first is that
controls manifest through changing the location of the guard (as opposed to
changing only the reset). The second is that the location of the guard is
described by "external variables" while the goal is to control "internal
variables." As a simple test of this theory, orientation control of a bouncing
ball is explored; the ball is only controlled during impacts which are
exclusively position-dependent.
