  Model predictive control is a control approach that minimizes a stage cost
over a predicted system trajectory based on a model of the system and is
capable of handling state and input constraints. For uncertain models, robust
or adaptive methods can be used. Because the system model is used to calculate
the control law, the closed-loop behavior of the system and thus its
performance, measured by the sum of the stage costs, are related to the model
used. If it is adapted online, a performance bound is difficult to obtain and
thus the impact of model adaptation is mostly unknown. This work provides a
(worst-case) performance bound for a linear adaptive predictive control scheme
with a specific model parameter estimation. The proposed bound is expressed in
terms of quantities such as the initial system parameter error and the
constraint set, among others and can be calculated a priori. The results are
discussed in a numerical example.
