In this paper, we consider distributed estimation of linear, discrete-time dynamical systems monitored by a network of agents. We require the agents to exchange information with their neighbors only once per dynamical system time-scale and study the network topology sufficient for distributed observability. To this aim, we provide a novel measurement-based agent classification: Type-, and , which leads to the construction of specific graph topologies:and . In particular, in , every Type-agent has a direct connection to every other agent, whereas, in , every agent has a directed path to every Type-agent. With the help of these constructs, we formulate an estimator where measurement and predictor-fusion are implemented over and , respectively, and show that the proposed scheme leads to distributed observability, i.e., observability of the distributed estimator. In order to characterize the estimator further, we show that Type-agents only exist in systems with -rank (maximal rank of zero/non-zero pattern) deficient system matrices. In other words, systems with full -rank matrices only have Type-agents, and thus, a stronglyconnected (agent) network is sufficient for full -rank systems-by the definition of above; however strong-connectivity is not necessary, i.e., there exist weakly-connected networks that result in distributed observability. Furthermore, we show that for -rank deficient systems, measurement-fusion over is required, and predictor-fusion alone is insufficient. The approach taken in this paper is structural, i.e., we use the concept of structured systems theory and generic observability to derive the results. Finally, we provide an iterative method to compute the local estimator gain at each agent once the observability is ensured using the aforementioned construction.

We consider distributed inference in social networks where a phenomenon of interest evolves over a given social interaction graph, referred to as the social digraph. For inference, we assume that a network of agents monitors certain nodes in the social digraph and no agent may be able to perform inference within its neighborhood; the agents must rely on inter-agent communication. The key contributions of this paper include: (i) a novel construction of the distributed estimator and distributed observability from the first principles; (ii) a graph-theoretic agent classification that establishes the importance and role of each agent towards inference; (iii) characterizing the necessary conditions, based on the classification in (ii), on the agent network to achieve distributed observability. Our results are based on structured systems theory and are applicable to any parameter choice of the underlying system matrix as long as the social digraph remains fixed. In other words, any social phenomena that evolves (linearly) over a structure-invariant social digraph may be considered-we refer to such systems as Liner Structure-Invariant (LSI). The aforementioned contributions, (i)-(iii), thus, only require the knowledge of the social digraph (topology) and are independent of the social phenomena. We show the applicability of the results to several real-wold social networks, i.e. social influence among monks, networks of political blogs and books, and a co-authorship graph.

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There are many practical situations where it is desirable or even required to achieve stable convergence in the finite-time domain. In this paper, a simple distributed continuous-time protocol is introduced that guarantees finite-time consensus in networks of autonomous agents. Protocol convergence in weighted directed/undirected and fixed/switching networks is explored based on a Lyapunov analysis. The stability of the system and the solvability of the consensus algorithm are proved for network topologies that contain a spanning tree frequently enough over contiguous time intervals. The decision value for different topologies and for multi-rate integrator agents is investigated, and a novel approach is proposed to determine the leader subgroup of agents. Communication time-delay and chattering phenomenon in the system are assessed, and additionally some protocols with Lipschitz righthand sides are introduced. Herein, all proposed consensus strategies use a limited-gain control input to account for the physical limitation of control actuation devices, which, in general, are subject to amplitude saturation.

This paper models the cyber-social system as a cyber-network of agents monitoring states of individuals in a social network. The state of each individual is represented by a social node and the interactions among individuals are represented by a social link. In the cyber-network each node represents an agent and the links represent information sharing among agents. Agents make an observation of social states and perform distributed inference. In this direction, the contribution of this work is threefold: (i) A novel distributed inference protocol is proposed that makes no assumption on the rank of the underlying social system. This is significant as most protocols in the literature only work on full-rank systems. (ii) A novel agent classification is developed, where it is shown that connectivity requirement on the cyber-network differs for each type. This is particularly important in finding the minimal number of observations and minimal connectivity of the cyber-network as the next contribution. (iii) The cost-optimal design of cybernetwork constraint with distributed observability is addressed. This problem is subdivided into sensing cost optimization and networking cost optimization where both are claimed to be NPhard. We solve both problems for certain types of social networks and find polynomial-order solutions. Fig. 1. This figure shows a cyber-social system: a social system, represented by interaction of individuals over a social network, monitored by a cybernetwork of agents. In this figure, the social network may represent a consensus network or dynamics of opinions. The blue links from the social nodes to the cyber nodes represent the measurement or observation taken from the social states of individuals by the agents, and the intelligent units tracking and observing the state of individuals connected via, for example, a wireless network represent the cyber-network. Based on observed information, agents share sufficient information and perform distributed inference, and therefore, are able to globally track the state of all individuals in the social network.

In this paper, we consider the binary classification problem via distributed Support Vector Machines (SVMs), where the idea is to train a network of agents, with limited share of data, to cooperatively learn the SVM classifier for the global database. Agents only share processed information regarding the classifier parameters and the gradient of the local loss functions instead of their raw data. In contrast to the existing work, we propose a continuoustime algorithm that incorporates network topology changes in discrete jumps. This hybrid nature allows us to remove chattering that arises because of the discretization of the underlying CT process. We show that the proposed algorithm converges to the SVM classifier over time-varying weight balanced directed graphs by using arguments from the matrix perturbation theory.

Observability of complex systems/networks is the focus of this paper, which is shown to be closely related to the concept of contraction. Indeed, for observable network tracking it is necessary/sufficient to have one node in each contraction measured. Therefore, nodes in a contraction are equivalent to recover for loss of observability, implying that contraction size is a key factor for observability recovery. Here, using a polynomial order contraction detection algorithm, we analyze the distribution of contractions, studying its relation with key network properties. Our results show that contraction size is related to network clustering coefficient and degree heterogeneity. Particularly, in networks with power-law degree distribution, if the clustering coefficient is high there are less contractions with smaller size on average. The implication is that estimation/tracking of such systems requires less number of measurements, while their observational recovery is more restrictive in case of sensor failure. Further, in Small-World networks higher degree heterogeneity implies that there are more contractions with smaller size on average. Therefore, the estimation of representing system requires more measurements, and also the recovery of measurement failure is more limited. These results imply that one can tune the properties of synthetic networks to alleviate their estimation/observability recovery. ! 2. See [1], [6], [15] for extension to nonlinear case. 3. It should be noted that structural observability and graph theoretic method applied as a tool to solve network observability problem. See reference [1], [6] for more information.4. Note that many of stated references deal with dual problem of network controllability. The graph properties and notions can be simply redefined for network observability.

In this brief paper, a new consensus protocol based on the sign of innovations is proposed. Based on this protocol each agent only requires single-bit of information about its relative state to its neighboring agents. This is significant in real-time applications, since it requires less computation and/or communication load on agents. Using Lyapunov stability theorem the convergence is proved for networks having a spanning tree. Further, the convergence is shown to be in finite-time, which is significant as compared to most asymptotic protocols in the literature. Time-variant network topologies are also considered in this paper, and final consensus value is derived for undirected networks. Applications of the proposed consensus protocol in (i) 2D/3D rendezvous task, (ii) distributed estimation, (iii) distributed optimization, and (iv) formation control are considered and significance of applying this protocol is discussed. Numerical simulations are provided to compare the protocol with the existing protocols in the literature.