  Predictive control is frequently used for control problems involving
constraints. Being an optimization based technique utilizing a user specified
so-called stage cost, performance properties, i.e., bounds on the infinite
horizon accumulated stage cost, aside closed-loop stability are of interest. To
achieve good performance and to influence the region of attraction associated
with the prediction horizon, the terminal cost of the predictive controller's
optimization objective is a key design factor. Approximate dynamic programming
refers to one particular approximation paradigm that pursues iterative cost
adaptation over a state domain. Troubled by approximation errors, the
associated approximate optimal controller is, in general, not necessarily
stabilizing nor is its performance quantifiable on the entire approximation
domain. Using a parametric terminal cost trained via approximate dynamic
programming, a stabilizing predictive controller is proposed whose performance
can directly be related to cost approximation errors. The controller further
ensures closed-loop asymptotic stability beyond the training domain of the
approximate optimal controller associated to the terminal cost.
