Safe Output Feedback Improvement with Baselines

TL;DR

This paper introduces a method to improve data-driven control by minimizing baseline regret, reducing conservatism and variance in controllers through a two-step output feedback design using data-driven models and convex optimization.

Contribution

It proposes a novel baseline regret minimization approach for safe control improvement, combining data-driven system identification and model reference control.

Findings

Baseline regret minimization enhances controller performance.

The method reduces variance compared to traditional min-max approaches.

Numerical examples validate improved safety and efficiency.

Abstract

In data-driven control design, an important problem is to deal with uncertainty due to limited and noisy data. One way to do this is to use a min-max approach, which aims to minimize some design criteria for the worst-case scenario. However, a strategy based on this approach can lead to overly conservative controllers. To overcome this issue, we apply the idea of baseline regret, and it is seen that minimizing the baseline regret under model uncertainty can guarantee safe controller improvement with less conservatism and variance in the resulting controllers. To exemplify the use of baseline controllers, we focus on the output feedback setting and propose a two-step control design method; first, an uncertainty set is constructed by a data-driven system identification approach based on finite impulse response models; then a control design criterion based on model reference control is used. To solve the baseline regret optimization problem efficiently, we use a convex approximation of the criterion and apply the scenario approach in optimization. The numerical examples show that the inclusion of baseline regret indeed improves the performance and reduces the variance of the resulting controller.