  This paper proposes a novel control scheme, named self-reflective model
predictive control, which takes its own limitations in the presence of process
noise and measurement errors into account. In contrast to existing
output-feedback MPC and persistently exciting MPC controllers, the proposed
self-reflective MPC controller does not only propagate a matrix-valued state
forward in time in order to predict the variance of future state-estimates, but
it also propagates a matrix-valued adjoint state backward in time. This adjoint
state is used by the controller to compute and minimize a second order
approximation of its own expected loss of control performance in the presence
of random process noise and inexact state estimates. The properties of the
proposed controller are illustrated with a small but non-trivial case study.
