Learning in Networked Control Systems

Abstract: We design adaptive controller (learning rule) for a networked control system (NCS) in which data packets containing control information are transmitted across a lossy wireless channel. We propose Upper Confidence Bounds for Networked Control Systems (UCB-NCS), a learning rule that maintains confidence intervals for the estimates of plant parameters $(A_{(\star)},B_{(\star)})$, and channel reliability $p_{(\star)}$, and utilizes the principle of optimism in the face of uncertainty while making control decisions. We provide non-asymptotic performance guarantees for UCB-NCS by analyzing its "regret", i.e., performance gap from the scenario when $(A_{(\star)},B_{(\star)},p_{(\star)})$ are known to the controller. We show that with a high probability the regret can be upper-bounded as $\tilde{O}\left(C\sqrt{T}\right)$\footnote{Here $\tilde{O}$ hides logarithmic factors.}, where $T$ is the operating time horizon of the system, and $C$ is a problem dependent constant.