Data-driven distributionally robust control of partially observable jump linear systems

TL;DR

This paper introduces a data-driven, distributionally robust control method for partially observable jump linear systems, combining online mode estimation with adaptive control to ensure safety despite unknown transition probabilities.

Contribution

It develops a receding horizon estimator for mode and state inference that adapts online without exhaustive search, integrated with a robust controller that updates as more data is observed.

Findings

Estimator effectively identifies mode sequences and states in real-time.

Controller maintains safety despite transition probability uncertainties.

Performance improves with more observed mode transitions.

Abstract

We study safe, data-driven control of (Markov) jump linear systems with unknown transition probabilities, where both the discrete mode and the continuous state are to be inferred from output measurements. To this end, we develop a receding horizon estimator which uniquely identifies a sub-sequence of past mode transitions and the corresponding continuous state, allowing for arbitrary switching behavior. Unlike traditional approaches to mode estimation, we do not require an offline exhaustive search over mode sequences to determine the size of the observation window, but rather select it online. If the system is weakly mode observable, the window size will be upper bounded, leading to a finite-memory observer. We integrate the estimation procedure with a simple distributionally robust controller, which hedges against misestimations of the transition probabilities due to finite sample sizes. As additional mode transitions are observed, the used ambiguity sets are updated, resulting in continual improvements of the control performance. The practical applicability of the approach is illustrated on small numerical examples.