  Stability under model predictive control (MPC) schemes is frequently ensured
by terminal ingredients. Employing a (control) Lyapunov function as the
terminal cost constitutes a common choice. Learning-based methods may be used
to construct the terminal cost by relating it to, for instance, an
infinite-horizon optimal control problem in which the optimal cost is a
Lyapunov function. Value iteration, an approximate dynamic programming (ADP)
approach, refers to one particular cost approximation technique. In this work,
we merge the results of terminally unconstrained predictive control and
approximate value iteration to draw benefits from both fields. A prediction
horizon is derived in dependence on different factors such as
approximation-related errors to render the closed-loop asymptotically stable
further allowing a suboptimality estimate in comparison to an infinite horizon
optimal cost. The result extends recent studies on predictive control with
ADP-based terminal costs, not requiring a local initial stabilizing controller.
We compare this controller in simulation with other terminal cost options to
show that the proposed approach leads to a shorter minimal horizon in
comparison to previous results.
