  This paper is about a real-time model predictive control (MPC) algorithm for
a particular class of model based controllers, whose objective consists of a
nominal tracking objective and an additional learning objective. Here, the
construction of the learning term is based on economic optimal experiment
design criteria. It is added to the MPC objective in order to excite the system
from time-to-time on purpose in order to improve the accuracy of the state and
parameter estimates in the presence of incomplete or noise affected
measurements. A particular focus of this paper is on so-called self-reflective
model predictive control schemes, which have the property that the additional
learning term can be interpreted as the expected loss of optimality of the
controller in the presence of random measurement errors. The main contribution
of this paper is a formulation-tailored algorithm, which exploits the
particular structure of self-reflective MPC problems in order to speed-up the
online computation. It is shown that, in contrast to generic state-of-the-art
optimal control problem solvers, the proposed algorithm can solve the
self-reflective optimization problems with reasonable additional computational
effort and in real-time. The advantages of the proposed real-time scheme are
illustrated by applying the algorithm to a nonlinear process control problem in
the presence of measurement errors and process noise.
