Data-Driven Predictive Control for Stochastic Descriptor Systems: An Innovation-Based Approach Handling Non-Causal Dependencies

Descriptor systems arise naturally in real-world applications governed by algebraic constraints, such as power networks, robotics and chemical processes. When a descriptor model contains a nontrivial nilpotent block, the discrete-time input--output map may be improper: the current output depends on future inputs and, in the stochastic case, on future noise terms. This letter proposes a data-driven predictive control framework for stochastic descriptor systems that handles these non-causal dependencies without explicitly identifying system matrices. The key idea is to split fast subsystem into noise-driven and input-driven parts, and then combine the former with the slow subsystem such that an innovation-driven Kalman filter can be appropriately defined to reformulate the stochastic descriptor system into an innovation-driven form. Based on this, a new behavioral system representation is derived, which inspires a data-driven innovation-based multi-step output predictor and a practical Inno-DeePC algorithm that enables data-driven predictive control design without known system matrices while implicitly handling algebraic constraints. Numerical experiments on a DC microgrid demonstrate the effectiveness of the proposed approach.