Data-Driven Predictive Control Using Closed-Loop Data: An Instrumental Variable Approach

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 letter, we propose a new DDPC method using closed-loop data by means of instrumental variables (IVs). We point out that the original DDPC fails to represent all admissible trajectories due to feedback control. By drawing from closed-loop subspace identification, the use of two forms of IVs is suggested to address this issue 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.