Data-Driven Tube-Based Stochastic Predictive Control

A powerful result from behavioral systems theory known as the fundamental lemma allows for predictive control akin to Model Predictive Control (MPC) for linear time-invariant (LTI) systems with unknown dynamics purely from data. While most data-driven predictive control literature focuses on robustness with respect to measurement noise, only a few works consider exploiting probabilistic information of disturbances for performance-oriented control as in stochastic MPC. This work proposes a novel data-driven stochastic predictive control scheme for chance-constrained LTI systems subject to measurement noise and additive stochastic disturbances. In order to render the otherwise stochastic and intractable optimal control problem deterministic, our approach leverages ideas from tube-based MPC by decomposing the state into a deterministic nominal state driven by inputs and a stochastic error state affected by disturbances. Satisfaction of original chance constraints is guaranteed by tightening nominal constraints probabilistically with respect to additive disturbances and robustly with respect to measurement noise. The resulting data-driven receding horizon optimal control problem is lightweight, recursively feasible, and renders the closed loop input-to-state stable in the presence of both additive disturbances and measurement noise. We demonstrate the effectiveness of the proposed approach in a simulation example.