  Current data-driven predictive control (DDPC) methods heavily rely on data
collected in open-loop operation with elaborate design of inputs. However, due
to safety or economic concerns, systems may have to be under feedback control,
where only closed-loop data are available. In this context, it remains
challenging to implement DDPC using closed-loop data. In this paper, we propose
a new DDPC method using closed-loop data by means of instrumental variables
(IVs). By drawing from closed-loop subspace identification, the use of two
forms of IVs is suggested to address the closed-loop issues caused by feedback
control and the correlation between inputs and noise. Furthermore, a new DDPC
formulation with a novel IV-inspired regularizer is proposed, where a balance
between control cost minimization and weighted least-squares data fitting can
be made for improvement of control performance. Numerical examples and
application to a simulated industrial furnace showcase the improved performance
of the proposed DDPC based on closed-loop data.
