A non-smooth control law and time-optimality notions for the acrobot

We propose a discontinuous control law to pump energy into the acrobot system to place the system at a certain energy level. Filippov calculus is used to establish convergence of the system trajectory to the desired energy set. The bang - bang nature of the control law prompts us to investigate whether the energy is pumped in minimum time. We then present necessary conditions for time optimality.