  Adaptive Horizon Model Predictive Control (AHMPC) is a scheme for varying as
needed the horizon length of Model Predictive Control (MPC). Its goal is to
achieve stabilization with horizons as small as possible so that MPC can be
used on faster or more complicated dynamic processes. Beside the standard
requirements of MPC including a terminal cost that is a control Lyapunov
function, AHMPC requires a terminal feedback that turns the control Lyapunov
function into a standard Lyapunov function in some domain around the operating
point. But this domain need not be known explicitly. MPC does not compute
off-line the optimal cost and the optimal feedback over a large domain instead
it computes these quantities on-line when and where they are needed. AHMPC does
not compute off-line the domain on which the terminal cost is a control
Lyapunov function instead it computes on-line when a state is in this domain.
