  Model predictive control (MPC) schemes are commonly designed with fixed,
i.e., time-invariant, horizon length and cost functions. If no stabilizing
terminal ingredients are used, stability can be guaranteed via a sufficiently
long horizon. A suboptimality index can be derived that gives bounds on the
performance of the MPC law over an infinite-horizon (IH). While for
time-invariant schemes such index can be computed offline, less attention has
been paid to time-varying strategies with adapting cost function which can be
found, e.g., in learning-based optimal control. This work addresses the
performance bounds of nonlinear MPC with stabilizing horizon and time-varying
terminal cost. A scheme is proposed that uses the decay of the optimal
finite-horizon cost and convolutes a history stack to predict the bounds on the
IH performance. Based on online information on the decay rate, the performance
bound estimate is improved while the terminal cost is adapted using methods
from adaptive dynamic programming. The adaptation of the terminal cost leads to
performance improvement over a time-invariant scheme with the same horizon
length. The approach is demonstrated in a case study.
