This brief examines bipartite consensus problem on matrix-valued weighted networks. First, it is shown that such networks achieve if and only the null space of Laplacian spanned by a Gauge transformation, extending results for scalar-valued Second, structurally balanced network has "positive-negative spanning tree," then can be achieved. Lastly, we show in case where edges are either positive definite or negative matrices, achieved balanced. Simulation provided to demonstrate these...

Multi-agent consensus algorithms have emerged as foundational tools across a spectrum of applications and matrix-weighted ones are capable characterizing cross-dimensional interdependence. Yet, their potential is often shadowed by pressing concern: the privacy agents' initial values, which frequently represent sensitive data or proprietary information. A computationally light privacy-preserving mechanism for average (MAC) proposed in response to concern privacy. In mechanism, states first...

This article examines the consensus problem on matrix-weighted undirected switching networks. First, we introduce integral network for analyzing such Under mild assumptions pattern of a sequence networks, conditions under which average can be achieved are then provided. It is shown that existence positive spanning tree in associated plays crucial role achieving consensus. In particular, periodic necessary and sufficient reaching obtained from an algebraic perspective. Simulation results...

In this paper, we examine the properties of Laplacian matrix defined on signed networks, referred to as matrix, from a graph-theoretic perspective. The connection between stability with cut set network is established. This then followed by relating and number negative eigenvalues negatively weighted edges in network. order stabilize dynamics, distributed diagonal compensation approach proposed; show that closely related structural balance Furthermore, influence external input exerted...

This letter examines the controllability of matrix-weighed networks from a graph-theoretic perspective. As distinct scalar-weighted networks, rank weight matrices introduce additional intricacies into characterizing dimension controllable subspace for such networks. Specifically, we investigate how definiteness matrices, encoding generalized characterization inter-agent connectivity on matrix-weighted influences lower and upper bounds associated subspaces. We show that bound is determined by...

This article examines the distributed nonconvex optimization problem with structured objective functions and coupled convex inequality constraints on static networks. A continuous-time primal-dual algorithm is proposed to solve problem. We use canonical transformation Lagrange multiplier method reformulate as a convex–concave saddle point computation problem, which subsequently solved by employing projected subgradient method. Sufficient conditions that guarantee global optimality of...

Bin-packing problem (BPP) is a typical combinatorial optimization whose decision-making process NP-hard. This article examines BPPs in varying environments, where random number and shape of items are to be packed different instances. The objective find unified model derive optimal decision that maximizes the utilization bins. To this end, by mimicking experience-based reasoning humans, proposes novel brain-inspired experience reinforcement model, which takes advantage both biological...

This paper examines the event-triggered global consensus of matrix-weighted networks subject to actuator saturation. A distributed protocol design is proposed for this category guarantee its both communication and It shown that largest singular value matrix-valued edge weights plays a crucial role in network performance, which renders framework more general than existing results are only applicable scalar-weighted networks. Conditions under can be guaranteed leaderless multi-agent derived....

In this paper, we consider distributed convex optimization problems on multi-agent networks. We develop and analyze the gradient method which allows each agent to compute its dynamic stepsize by utilizing time-varying estimate of local function value at global optimal solution. Our approach can be applied both synchronous asynchronous communication protocols. Specifically, propose subgradient with uncoordinated stepsizes (DS-UD) algorithm for protocol AsynDGD protocol. Theoretical analysis...

Achieving consensus via nearest neighbor rules is an important prerequisite for multiagent networks to accomplish collective tasks. A common assumption in setup that each agent interacts with all its neighbors. This article examines whether network functionality and performance can be maintained—and even enhanced—when agents interact only a subset of their respective (available) As shown this article, the answer inquiry affirmative. In direction, we show by exploring monotonicity property...

Abstract The topology and dynamics of a complex network shape its functionality. However, the topologies many large-scale networks are either unavailable or incomplete. Without explicit knowledge topology, we show how data generated from can be utilised to infer tempo centrality, which is proposed quantify influence nodes in consensus network. We that centrality used construct an accurate estimate both propagation rate exerted on Kirchhoff index underlying graph. Moreover, also encodes...

In this work, a novel metric is introduced in order to measure the influence of one subgroup agents on another consensus-type networks. The solely graph-depended and its value can be calculated from normalized eigenvector corresponding second smallest eigenvalue graph Laplacian, known as Fiedler vector widely used partitioning algorithms. We also examine for influenced consensus model where external could attach network evolution agents' states. It shown that proposed similar centrality...

This paper examines the event-triggered consensus problem of multi-agent system on signed networks. An event-based distributed control protocol is proposed for multiagent networks where dynamics each agent characterized by a controllable linear time-invariant ( A, B). By exploring Gauge transformation between Laplacian matrix and matrix, we show that bipartite trivial can be achieved, respectively, in terms structural balance underlying network. Furthermore, Zeno phenomenon closed-loop shown...

In this paper we consider the aggregation stability problem of a multi-agents system under network, among agents there are nonlinear attactive/repulsive forces. Our work generalizes results given by Gazi and Passino [1] Chu, Wang Chen [2], [3], [4] into very general setting. It shows that in undirect communication network will asymptotically form cohesive cluster with finite size if attraction repulsion functions satisfy some mild assumptions. We give several numerical simulations...

In this work, we consider the consensus problem of multi-agent system over matrix-weighted networks using an event-triggered mechanism. An coordination strategy is proposed to steer generalized category systems towards bipartite state. The triggering condition periodically checked and distributed in sense that event detector only uses neighbors' information local computation at discrete sampling instants. Moreover, it shown closely related spectrum matrix-valued weights corresponding edges...

In this paper the consensus of multi-agent system in directed network, where agent is described by a second-order dynamics, studied. The control protocol depends on two parameters, i.e. position-cooperative parameter w <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> >0 and velocity-cooperation xmlns:xlink="http://www.w3.org/1999/xlink">v</inf> >0, Laplacian associated with communication network. definition slightly different from that...

The structural balance plays a fundamental role in networked systems with both attractive and repulsive interactions, which can be characterized by signed network. In this paper, we show that the ensemble of type interaction network inferred from eigenvector Laplacian matrix. Also, it has been shown graph, derived graph Cartesian product factor graphs, is structurally balanced if only its factors are balanced. According to theoretical results, verification prediction presented data-driven...