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Adaptive Horizon Model Predictive Control (AHMPC) is a scheme for varying the horizon length of Model Predictive Control (MPC) as needed. Its goal is to achieve stabilization with horizons as small as possible so that it can be used on faster or more complicated dynamic process. 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. Just as 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. AHMPC verifies in real time that stabilization is being achieved. This is particularly important when dealing with non-linear systems because the nonlinear programs that MPC passes to the nonlinear program solver are typically nonconvex. Therefore the solver may return local rather than global solutions and these may fail to be stabilizing. AHMPC detects when the solutions are not stabilizing. If so there is a need to pass different initial guesses to the solver to find global solutions or at least local solutions that are stabilizing.