Data-Driven Robust Control Using Prediction Error Bounds Based on Perturbation Analysis

TL;DR

This paper introduces a data-driven control method for linear systems that accounts for measurement noise by computing prediction error bounds, enabling robust control with guaranteed constraint satisfaction.

Contribution

It proposes a novel approach to design experiments and compute bounds on prediction errors, facilitating robust control under bounded noise in a data-driven framework.

Findings

Achieves constraint satisfaction despite measurement noise

Provides bounds on suboptimality gap of control solutions

Demonstrates effectiveness through numerical experiments

Abstract

For linear systems, many data-driven control methods rely on the behavioral framework, using historical data of the system to predict the future trajectories. However, measurement noise introduces errors in predictions. When the noise is bounded, we propose a method for designing historical experiments that enable the computation of an upper bound on the prediction error. This approach allows us to formulate a minimax control problem where robust constraint satisfaction is enforced. We derive an upper bound on the suboptimality gap of the resulting control input sequence compared to optimal control utilizing accurate measurements. As demonstrated in numerical experiments, the solution derived by our method can achieve constraint satisfaction and a small suboptimality gap despite the measurement noise.