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.
Categories: cs.LG cs.IT math.DS math.IT stat.ML