  Model predictive control (MPC) for uncertain systems in the presence of hard
constraints on state and input is a non-trivial problem, and the challenge is
increased manyfold in the absence of state measurements. In this paper, we
propose an adaptive output feedback MPC technique, based on a novel combination
of an adaptive observer and robust MPC, for single-input single-output
discrete-time linear time-invariant systems. At each time instant, the adaptive
observer provides estimates of the states and the system parameters that are
then leveraged in the MPC optimization routine while robustly accounting for
the estimation errors. The solution to the optimization problem results in a
homothetic tube where the state estimate trajectory lies. The true state
evolves inside a larger outer tube obtained by augmenting a set, invariant to
the state estimation error, around the homothetic tube sections. The proof for
recursive feasibility for the proposed `homothetic and invariant' two-tube
approach is provided, along with simulation results on an academic system.
