Stochastic Data-driven Predictive Control of Linear Systems with Sub-Gaussian Disturbances using Causal Predictors

Abstract: We present a stochastic data-driven predictive control (DPC) framework for discrete-time linear time-invariant systems subject to sub-Gaussian additive disturbances based solely on input--output data. In contrast to related methods that rely on exact disturbance data or at least sample generation for closed-loop guarantees, the proposed approach leverages a disturbance data estimate. By enforcing consistency of the disturbance data estimate with the available input--output data and system class, we first identify data-driven and provably causal subspace predictors for use in DPC. Then, we analyze statistical properties of the corresponding prediction error, yielding tightened constraints for the nominal predictions that guarantee satisfaction of chance constraints. The proposed DPC scheme comes with guarantees on recursive feasibility and conditional chance constraint satisfaction in closed-loop under standard assumptions. A numerical evaluation study demonstrates the performance of the proposed controller.