  Incorporating pattern-learning for prediction (PLP) in many discrete-time or
discrete-event systems allows for computation-efficient controller design by
memorizing patterns to schedule control policies based on their future
occurrences. In this paper, we demonstrate the effect of PLP by designing a
controller architecture for a class of linear Markovian jump systems (MJS)
where the aforementioned ``patterns'' correspond to finite-length sequences of
modes. In our analysis of recurrent patterns, we use martingale theory to
derive closed-form solutions to quantities pertaining to the occurrence of
patterns: 1) the expected minimum occurrence time of any pattern from some
predefined collection, 2) the probability of a pattern being the first to occur
among the collection. Our method is applicable to real-world dynamics because
we make two extensions to common assumptions in prior pattern-occurrence
literature. First, the distribution of the mode process is unknown, and second,
the true realization of the mode process is not observable. As demonstration,
we consider fault-tolerant control of a dynamic topology-switching network, and
empirically compare PLP to two controllers without PLP: a baseline based on the
novel System Level Synthesis (SLS) approach and a topology-robust extension of
the SLS baseline. We show that PLP is able to reject disturbances as
effectively as the topology-robust controller at reduced computation time and
control effort. We discuss several important tradeoffs, such as the size of the
pattern collection and the system scale versus the accuracy of the mode
predictions, which show how different PLP implementations affect stabilization
and runtime performance.
