Towards data-driven stochastic predictive control

Data-driven predictive control based on the fundamental lemma by Willems et al. is frequently considered for deterministic LTI systems subject to measurement noise. However, little has been done on data-driven stochastic control. In this paper, we propose a data-driven stochastic predictive control scheme for LTI systems subject to possibly unbounded additive process disturbances. Based on a stochastic extension of the fundamental lemma and leveraging polynomial chaos expansions, we construct a data-driven surrogate optimal control problem (OCP). Moreover, combined with an online selection strategy of the initial condition of the OCP, we provide sufficient conditions for recursive feasibility and for stability of the proposed data-driven predictive control scheme. Finally, two numerical examples illustrate the efficacy and closed-loop properties of the proposed scheme for process disturbances governed by different distributions.

Automated summary

Data-driven stochastic predictive control scheme is proposed for LTI systems subject to unbounded additive process disturbances. A data-driven surrogate optimal control problem is constructed using a stochastic extension of the fundamental lemma and leveraging polynomial chaos expansions. Sufficient conditions for recursive feasibility and stability of the proposed scheme are provided, along with an online selection strategy of the initial condition. Numerical examples illustrate the efficacy and closed-loop properties of the proposed scheme for process disturbances governed by different distributions.