Robustness of Control Design via Bayesian Learning
This work addresses control design robustness for unstable systems, but it is incremental as it applies known Bayesian learning techniques to a specific control task.
The paper tackled the problem of designing robust linear controllers for unstable stochastic systems by comparing deterministic methods with Bayesian learning approaches that account for uncertainties, showing that Bayesian learning improved robustness under perturbations.
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.