Robustness of Control Design via Bayesian Learning

TL;DR

This paper explores how Bayesian learning enhances the robustness of control design, specifically in stabilizing unstable stochastic systems, by comparing traditional and Bayesian approaches to controller synthesis.

Contribution

It demonstrates the application of Bayesian learning to control search, showing improved robustness in stabilizing uncertain stochastic systems compared to deterministic methods.

Findings

Bayesian learning improves robustness in control design.

Bayesian approach effectively handles uncertainties in system parameters.

Comparison shows Bayesian method outperforms deterministic control in stability tasks.

Abstract

In the realm of supervised learning, Bayesian learning has shown robust predictive capabilities under input and parameter perturbations. Inspired by these findings, we demonstrate the robustness properties of Bayesian learning in the control search task. We seek to find a linear controller that stabilizes a one-dimensional open-loop unstable stochastic system. We compare two methods to deduce the controller: the first (deterministic) one assumes perfect knowledge of system parameter and state, the second takes into account uncertainties in both and employs Bayesian learning to compute a posterior distribution for the controller.