Robust Data-Driven Predictive Control for Unknown Linear Systems With Bounded Disturbances

This paper presents a robust data-driven predictive control (RDPC) framework for linear time-invariant (LTI) systems affected by bounded disturbances and measurement noise. Unlike traditional model-based approaches, the proposed method relies solely on input-stateoutput (ISO) data without requiring prior system identification. Given that multiple systems can be consistent with the collected data due to disturbances and noise, a set of all possible systems using quadratic matrix inequalities (QMIs) is constructed. The RDPC scheme is then formulated as an optimization problem that minimizes an upper bound on the control objective while ensuring robust constraint satisfaction for all systems in the set. Unlike the existing robust data-driven model predictive control methods based on behavioral system theory, the proposed method does not require the pre-collected data to satisfy the persistently exciting condition of a sufficiently high order. It only needs the stabilizability of the LTI system to be controlled. The proposed approach is further extended for systems where the state is unmeasurable. By reformulating the problem using an autoregressive exogenous (ARX) model, a dynamic output feedback controller that leverages input-output (IO) data directly is designed. The effectiveness of the proposed methods is validated through a case study on an unstable batch reactor, demonstrating comparable performance to model-based robust MPC and data-driven MPC approaches while reducing conservatism and computational complexity.