Stochastic Data-Driven Predictive Control: Chance-Constraint Satisfaction with Identified Multi-step Predictors
Haldun Balim, Andrea Carron, Melanie N. Zeilinger, Johannes Köhler
TL;DR
This work tackles enforcing chance constraints for uncertain linear systems with noisy outputs by introducing a data-driven stochastic MPC built on multi-step predictors. It identifies multi-step predictor parameters from input-output data using Kalman innovation form based maximum likelihood estimation, and propagates uncertainty through the predictions via a surrogate state-space model. A constraint tightening strategy is then formulated as a convex second-order cone program that guarantees chance constraint satisfaction despite parametric uncertainty, with a novel nonuniform tightening that is independent of the parameter dimension. A numerical example on a mass-spring-damper chain shows significantly reduced conservatism compared with sequential propagation and ellipsoidal-uncertainty approaches, while maintaining reliability in constraint satisfaction. The approach offers a practical pathway for data-driven propulsion of MSP-based MPC in safety-critical settings and motivates future work on receding-horizon guarantees and nonlinear extensions.
Abstract
We propose a novel data-driven stochastic model predictive control framework for uncertain linear systems with noisy output measurements. Our approach leverages multi-step predictors to efficiently propagate uncertainty, ensuring chance constraint satisfaction. In particular, we present a strategy to identify multi-step predictors and quantify the associated uncertainty using a surrogate (data-driven) state space model. Then, we utilize the derived distribution to formulate a constraint tightening that ensures chance constraint satisfaction despite the parametric uncertainty. A numerical example highlights the reduced conservatism of handling parametric uncertainty in the proposed method compared to state-of-the-art solutions.