Distributionally Robust Stochastic Data-Driven Predictive Control with Optimized Feedback Gain

TL;DR

This paper introduces a distributionally robust data-driven predictive control method for stochastic LTI systems with partial observations, optimizing feedback gain and ensuring safety constraints without assuming Gaussian noise.

Contribution

It relaxes Gaussian noise assumptions and optimizes feedback gain within the control policy, advancing data-driven stochastic control methods.

Findings

Control inputs match model-based stochastic predictive control under ideal conditions.

Enhanced performance demonstrated through simulation studies.

Distributionally robust safety constraints improve reliability.

Abstract

We consider the problem of direct data-driven predictive control for unknown stochastic linear time-invariant (LTI) systems with partial state observation. Building upon our previous research on data-driven stochastic control, this paper (i) relaxes the assumption of Gaussian process and measurement noise, and (ii) enables optimization of the gain matrix within the affine feedback policy. Output safety constraints are modelled using conditional value-at-risk, and enforced in a distributionally robust sense. Under idealized assumptions, we prove that our proposed data-driven control method yields control inputs identical to those produced by an equivalent model-based stochastic predictive controller. A simulation study illustrates the enhanced performance of our approach over previous designs.