  Model predictive control (MPC) is a widely used modern control technique with
numerous successful application in diverse areas. Much of this success is due
to the ability of MPC to enforce state and control constraints, which are
crucial in many applications of control. In order to avoid the need for an
observer, output-feedback model predictive control with online identification
(OFMPCOI) uses the block observable canonical form whose state consists of past
values of the control inputs and measured outputs. Online identification is
performed using recursive least squares (RLS) with variable-rate forgetting.
The article describes the algorithmic details of OFMPCOI and numerically
investigates its performance through a collection of numerical examples that
highlight various control challenges, such as model order uncertainty, sensor
noise, prediction horizon, stabilization, magnitude and move-size saturation,
and stabilization. The numerical examples are used to probe the performance of
OFMPCOI in terms of persistency, consistency, and exigency. Since OFMPCOI does
not employ a separate control perturbation to enhance persistency, the focus is
on self-generated persistency during transient operation. For closed-loop
identification using RLS, sensor noise gives rise to bias in the identified
model, and the goal is to determine the effect of the lack of consistency.
Finally, the numerical examples reveal exigency, which is the extent to which
the online identification emphasizes model characteristics that are most
relevant to meeting performance objectives.
