Control of large-scale networked systems often necessitates the availability of complex models for the interactions amongst the agents. However, in many applications building accurate models of these interactions might be prohibitive due to the curse of dimensionality or their inherent complexity. In the meantime, data-guided control methods can circumvent model complexity by directly synthesizing the controller from the observed data. In this paper, we propose a distributed Q-learning algorithm to design a feedback mechanism given an underlying graph structure parameterizing the agents' communication. We assume that the distributed nature of the system arises from a common cost and show that for the particular case of identical dynamically decoupled systems, the learned controller converges to the optimal Linear Quadratic Regulator controller for each subsystem. We provide a convergence analysis and verify the result with an example.

Signed networks have been a topic of recent interest in the network control community as they allow studying antagonistic interactions in multi-agent systems. Although dynamical characteristics of signed networks have been wellstudied, notions such as controllability and stabilizability for signed networks for protocols such as consensus are missing in the literature. Classically, graph automorphisms with respect to the input nodes have been used to characterize uncontrollability of consensus networks. In this paper, we show that in addition to the graph symmetry, the topological property of structural balance facilitates the derivation of analogous sufficient conditions for uncontrollability for signed networks. In particular, we provide an analysis which shows that a gauge transformation induced by structural balance allows symmetry arguments to hold for signed consensus networks. Lastly, we use fractional automorphisms to extend our observations to output controllability and stabilizability of signed networks.

Recently, data-driven methods for control of dynamic systems have received considerable attention in system theory and machine learning as they provide a mechanism for feedback synthesis from the observed time-series data. However learning, say through direct policy updates, often requires assumptions such as knowing a priori that the initial policy (gain) is stabilizing, e.g., when the open-loop system is stable. In this paper, we examine online regulation of (possibly unstable) partially unknown linear systems with no a priori assumptions on the initial controller. First, we introduce and characterize the notion of "regularizability" for linear systems that gauges the capacity of a system to be regulated in finite-time in contrast to its asymptotic behaviour (commonly characterized by stabilizability/controllability). Next, having access only to the input matrix, we propose the Data-Guided Regulation (DGR) synthesis that-as its name suggests-regulates the underlying states while also generating informative data that can subsequently be used for data-driven stabilization or system identification (sysID). The analysis is also related in spirit, to the spectrum and the "instability number" of the underlying linear system, a novel geometric property studied in this work. We further elucidate our results by considering special structures for system parameters as well as boosting the performance of the algorithm via a rank-one matrix update using the discrete nature of data collection in the problem setup. Finally, we demonstrate the utility of the proposed approach via an example involving direct (online) regulation of the X-29 aircraft.

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