On Min-Max Robust Data-Driven Predictive Control Considering Non-Unique Solutions to Behavioral Representation

Direct data-driven control methods are known to be vulnerable to uncertainty in stochastic systems. In this paper, we propose a new robust data-driven predictive control (DDPC) framework. By analyzing non-unique solutions to behavioral representation, we gain insight into the inherent lack of robustness in subspace predictive control (SPC) and its projection-based regularized variant. This stimulates us to construct an uncertainty set that captures all admissible output trajectories deviating from nominal subspace predictions, which results in a min-max robust formulation of DDPC that endows control sequences with robustness against such unknown deviations. We establish theoretical performance guarantees under bounded additive noise and develop tractable convex reformulations. To mitigate the conservatism of robust design, a feedback robust DDPC scheme is further proposed by incorporating an affine feedback policy. Simulation studies show that the proposed methods effectively robustify SPC and outperform the projection-based regularization.