arXiv subjects

Haibin Shao

Publications and source records attributed to Haibin Shao.

15 recordsLinked to original sources

arXiv2026

Subspace Consensus of Matrix-Weighted Networks

This paper investigates the subspace consensus problem of matrix-weighted multi-agent networks, where each agent possesses a vector-valued state in $\mathbb{R}^{d}$ and interactions between neighboring agents are characterized by matrix-valued edge weights. Besides all dimensions of the agent states achieve full-state consensus, many practical applications appeal that agents are required to agree only on certain dimensions while maintaining desired relative configurations in the remaining ones. To address this gap, we introduce the concept of subspace consensus. A matrix-weighted network is said to achieve subspace consensus on a subspace $\mathbb{V}\subseteq\mathbb{R}^{d}$ if the projection of the agents' state differences onto $\mathbb{V}$ asymptotically converges to zero. This definition renders the traditional consensus as a special case when $\mathbb{V}=\mathbb{R}^{d}$. From an algebraic perspective, we derive necessary and sufficient conditions for subspace consensus by analyzing the interplay between the null spaces of edge weights. From a topological perspective, we present sufficient conditions characterized by $\mathbb{V}$-connectivity and the existence of a $\mathbb{V}$-spanning tree, as well as necessary conditions based on graph cuts. Furthermore, we provide refined necessary and sufficient conditions specifically for tree networks. This work uncovers a fundamental capability inherent to matrix-weighted networks and establishes a systematic framework for analyzing agreement behaviors on prescribed subspaces.

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arXiv2024

Sufficient Condition on Bipartite Consensus of Weakly Connected Matrix-weighted Networks

Recent advances in bipartite consensus on matrix-weighted networks, where agents are divided into two disjoint sets with those in the same set agreeing on a certain value and those in different sets converging to opposite values, have highlighted its potential applications across various fields. Traditional approaches often depend on the existence of a positive-negative spanning tree in matrix-weighted networks to achieve bipartite consensus, which greatly restricts the use of these approaches in engineering applications. This study relaxes that assumption by allowing weak connectivity within the network, where paths can be weighted by semidefinite matrices. By analyzing the algebraic constraints imposed by positive-negative trees and semidefinite paths, we derive new sufficient conditions for achieving bipartite consensus. Our findings are validated by numerical simulations.

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arXiv2023

Sufficient Conditions on Bipartite Consensus of Weakly Connected Matrix-weighted Networks

Recent advancements in bipartite consensus, a scenario where agents are divided into two disjoint sets with agents in the same set agreeing on a certain value and those in different sets agreeing on opposite or specifically related values, have highlighted its potential applications across various fields. Traditional research typically relies on the presence of a positive-negative spanning tree, which limits the practical applicability of bipartite consensus. This study relaxes that assumption by allowing for weak connectivity within the network, where paths can be weighted by semidefinite matrices. By exploring the algebraic constraints imposed by positive-negative trees and semidefinite paths, we derive sufficient conditions for achieving bipartite consensus. Our theoretical findings are validated through numerical results.

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arXiv2023

Binary system modes of matrix-coupled multidimensional Kuramoto oscillators

Synchronization and desynchronization are the two ends on the spectrum of emergent phenomena that somehow often coexist in biological, neuronal, and physical networks. However, previous studies essentially regard their coexistence as a partition of the network units: those that are in relative synchrony and those that are not. In real-world systems, desynchrony bears subtler divisions because the interacting units are high-dimensional, like fish schooling with varying speeds in a circle, synchrony and desynchrony may occur to the different dimensions of the population. In this work, we show with an ensemble of multidimensional Kuramoto oscillators, that this property is generalizable to arbitrary dimensions: for a $d$ dimensional population, there exist $2^d$ system modes where each dimension is either synchronized or desynchronized, represented by a set of almost binary order parameters. Such phenomena are induced by a matrix coupling mechanism that goes beyond the conventional scalar-valued coupling by capturing the inter-dimensional dependence amongst multidimensional individuals, which arises naturally from physical, sociological and engineering systems. As verified by our theory, the property of the coupling matrix thoroughly affects the emergent system modes and the phase transitions toward them. By numerically demonstrating that these system modes are interchangeable through matrix manipulation, we also observe explosive synchronization/desynchronization that is induced without the conditions that are previously deemed essential. Our discovery provides theoretical analogy to the cerebral activity where the resting state and the activated state coexist unihemispherically, it also evokes a new possibility of information storage in oscillatory neural networks.

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arXiv2022

Vector-valued Privacy-Preserving Average Consensus

Achieving average consensus without disclosing sensitive information can be a critical concern for multi-agent coordination. This paper examines privacy-preserving average consensus (PPAC) for vector-valued multi-agent networks. In particular, a set of agents with vector-valued states aim to collaboratively reach an exact average consensus of their initial states, while each agent's initial state cannot be disclosed to other agents. We show that the vector-valued PPAC problem can be solved via associated matrix-weighted networks with the higher-dimensional agent state. Specifically, a novel distributed vector-valued PPAC algorithm is proposed by lifting the agent-state to higher-dimensional space and designing the associated matrix-weighted network with dynamic, low-rank, positive semi-definite coupling matrices to both conceal the vector-valued agent state and guarantee that the multi-agent network asymptotically converges to the average consensus. Essentially, the convergence analysis can be transformed into the average consensus problem on switching matrix-weighted networks. We show that the exact average consensus can be guaranteed and the initial agents' states can be kept private if each agent has at least one "legitimate" neighbor. The algorithm, involving only basic matrix operations, is computationally more efficient than cryptography-based approaches and can be implemented in a fully distributed manner without relying on a third party. Numerical simulation is provided to illustrate the effectiveness of the proposed algorithm.

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arXiv2022

Dynamic Event-Triggered Consensus of Multi-agent Systems on Matrix-weighted Networks

This paper examines the event-triggered consensus of the multi-agent system on matrix-weighted networks, where the interdependencies among higher-dimensional states of neighboring agents are characterized by matrix-weighted edges in the network. Specifically, a novel distributed dynamic event-triggered coordination strategy is proposed for this category of generalized networks, in which an auxiliary system is employed for each agent to dynamically adjust the triggering threshold, which plays an essential role in guaranteeing that the triggering time sequence does not exhibit Zeno behavior. Distributed event-triggered control protocols are proposed to guarantee leaderless and leader-follower consensus for multi-agent systems on matrix-weighted networks, respectively. Remarkably, the spectrum of matrix-valued weights is crucial in event-triggered mechanism design for matrix-weighted networks, generalizing those results only applicable for scalar-weighted networks. The proposed approach allows each agent to broadcast and receive information only at its triggering instants. Finally, simulation examples are provided to demonstrate the theoretical results.

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arXiv2022

Structural Adaptivity of Directed Networks

Network structure plays a critical role in functionality and performance of network systems. This paper examines structural adaptivity of diffusively coupled, directed multi-agent networks that are subject to diffusion performance. Inspired by the observation that the link redundancy in a network may degrade its diffusion performance, a distributed data-driven neighbor selection framework is proposed to adaptively adjust the network structure for improving the diffusion performance of exogenous influence over the network. Specifically, each agent is allowed to interact with only a specific subset of neighbors while global reachability from exogenous influence to all agents of the network is maintained. Both continuous-time and discrete-time directed networks are examined. For each of the two cases, we first examine the reachability properties encoded in the eigenvectors of perturbed variants of graph Laplacian or SIA matrix associated with directed networks, respectively. Then, an eigenvector-based rule for neighbor selection is proposed to derive a reduced network, on which the diffusion performance is enhanced. Finally, motivated by the necessity of distributed and data-driven implementation of the neighbor selection rule, quantitative connections between eigenvectors of the perturbed graph Laplacian and SIA matrix and relative rate of change in agent state are established, respectively. These connections immediately enable a data-driven inference of the reduced neighbor set for each agent using only locally accessible data. As an immediate extension, we further discuss the distributed data-driven construction of directed spanning trees of directed networks using the proposed neighbor selection framework. Numerical simulations are provided to demonstrate the theoretical results.

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arXiv2022

Distributed Neighbor Selection in Multi-agent Networks

Achieving consensus via nearest neighbor rules is an important prerequisite for multi-agent networks to accomplish collective tasks. A common assumption in consensus setup is that each agent interacts with all its neighbors. This paper examines whether network functionality and performance can be maintained-and even enhanced-when agents interact only with a subset of their respective (available) neighbors. As shown in the paper, the answer to this inquiry is affirmative. In this direction, we show that by exploring the monotonicity property of the Laplacian eigenvectors, a neighbor selection rule with guaranteed performance enhancements, can be realized for consensus-type networks. For distributed implementation, a quantitative connection between entries of Laplacian eigenvectors and the "relative rate of change" in the state between neighboring agents is further established; this connection facilitates a distributed algorithm for each agent to identify "favorable" neighbors to interact with. Multi-agent networks with and without external influence are examined, as well as extensions to signed networks. This paper underscores the utility of Laplacian eigenvectors in the context of distributed neighbor selection, providing novel insights into distributed data-driven control of multi-agent systems.

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arXiv2022

Distributed Stabilization of Signed Networks via Self-loop Compensation

This paper examines the stability and distributed stabilization of signed multi-agent networks. Here, positive semidefiniteness is not inherent for signed Laplacians, which renders the stability and consensus of this category of networks intricate. First, we examine the stability of signed networks by introducing a novel graph-theoretic objective negative cut set, which implies that manipulating negative edge weights cannot change a unstable network into a stable one. Then, inspired by the diagonal dominance and stability of matrices, a local state damping mechanism is introduced using self-loop compensation. The self-loop compensation is only active for those agents who are incident to negative edges and can stabilize signed networks in a fully distributed manner. Quantitative connections between self-loop compensation and the stability of the compensated signed network are established for a tradeoff between compensation efforts and network stability. Necessary and/or sufficient conditions for predictable cluster consensus of compensated signed networks are provided. The optimality of self-loop compensation is discussed. Furthermore, we extend our results to directed signed networks where the symmetry of signed Laplacian is not free. The correlation between the stability of the compensated dynamics obtained by self-loop compensation and eventually positivity is further discussed. Novel insights into the stability of multi-agent systems on signed networks in terms of self-loop compensation are offered. Simulation examples are provided to demonstrate the theoretical results.

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arXiv2021

Event-triggered Consensus of Matrix-weighted Networks Subject to Actuator Saturation

The ubiquitous interdependencies among higher-dimensional states of neighboring agents can be characterized by matrix-weighted networks. This paper examines event-triggered global consensus of matrix-weighted networks subject to actuator saturation. Specifically, a distributed dynamic event-triggered coordination strategy, whose design involves sampled state of agents, saturation constraint and auxiliary systems, is proposed for this category of generalized network to guarantee its global consensus. Under the proposed event-triggered coordination strategy, sufficient conditions are derived to guarantee the leaderless and leader-follower global consensus of the multi-agent systems on matrix-weighted networks, respectively. The Zeno phenomenon can be excluded for both cases under the proposed coordination strategy. It turns out that the spectral properties of matrix-valued weights are crucial in event-triggered mechanism design for matrix-weighted networks with actuator saturation constraint. Finally, simulations are provided to demonstrate the effectiveness of proposed event-triggered coordination strategy. This work provides a more general design framework compared with existing results that are only applicable to scalar-weighted networks.

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arXiv2021

Independent dimensional phase transition on a two-dimensional Kuramoto model with matrix coupling

The high-dimensional generalization of the one-dimensional Kuramoto paradigm has been an essential step in bringing about a more faithful depiction of the dynamics of real-world systems. Despite the multi-dimensional nature of the oscillators in these generalized models, the interacting schemes so far have been dominated by a scalar factor unanimously between any pair of oscillators that leads eventually to synchronization on all dimensions. As a natural extension of the scalar coupling befitting for the one-dimensional case, we take a tentative step in studying numerically and theoretically the coupling mechanism of $2\times2$ real matrices on two-dimensional Kuramoto oscillators. One of the features stemmed from this new mechanism is that the matrix coupling enables the two dimensions of the oscillators to separate their transitions to either synchronization or desynchronization which has not been seen in other high-dimensional generalizations. Under various matrix configurations, the synchronization and desynchronization of the two dimensions combine into four qualitatively distinct modes of position and motion of the system. We demonstrate that as one matrix is morphed into another in a specific manner, the system mode also switches correspondingly either through continuous or explosive transitions of the order parameters, thus mimicking a range of behaviors in information science and biology.

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arXiv2021

Cluster Consensus on Matrix-weighted Switching Networks

This paper examines the cluster consensus problem of multi-agent systems on matrix-weighted switching networks. Necessary and/or sufficient conditions under which cluster consensus can be achieved are obtained and quantitative characterization of the steady-state of the cluster consensus are provided as well. Specifically, if the underlying network switches amongst finite number of networks, a necessary condition for cluster consensus of multi-agent system on switching matrix-weighted networks is firstly presented, it is shown that the steady-state of the system lies in the intersection of the null space of matrix-valued Laplacians corresponding to all switching networks. Second, if the underlying network switches amongst infinite number of networks, the matrix-weighted integral network is employed to provide sufficient conditions for cluster consensus and the quantitative characterization of the corresponding steady-state of the multi-agent system, using null space analysis of matrix-valued Laplacian related of integral network associated with the switching networks. In particular, conditions for the bipartite consensus under the matrix-weighted switching networks are examined. Simulation results are finally provided to demonstrate the theoretical analysis.

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arXiv2021

Characterizing Bipartite Consensus on Signed Matrix-Weighted Networks via Balancing Set

In contrast with the scalar-weighted networks, where bipartite consensus can be achieved if and only if the underlying signed network is structurally balanced, the structural balance property is no longer a graph-theoretic equivalence to the bipartite consensus in the case of signed matrix-weighted networks. To re-establish the relationship between the network structure and the bipartite consensus solution, the non-trivial balancing set is introduced which is a set of edges whose sign negation can transform a structurally imbalanced network into a structurally balanced one and the weight matrices associated with edges in this set have a non-trivial intersection of null spaces. We show that necessary and/or sufficient conditions for bipartite consensus on matrix-weighted networks can be characterized by the uniqueness of the non-trivial balancing set, while the contribution of the associated non-trivial intersection of null spaces to the steady-state of the matrix-weighted network is examined. Moreover, for matrix-weighted networks with a positive-negative spanning tree, necessary and sufficient condition for bipartite consensus using the non-trivial balancing set is obtained. Simulation examples are provided to demonstrate the theoretical results.

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arXiv2020

Consensus on Matrix-weighted Time-varying Networks

This paper examines the consensus problem on time-varying matrix-weighed undirected networks. First, we introduce the matrix-weighted integral network for the analysis of such networks. Under mild assumptions on the switching pattern of the time-varying network, necessary and/or sufficient conditions for which average consensus can be achieved are then provided in terms of the null space of matrix-valued Laplacian of the corresponding integral network. In particular, for periodic matrix-weighted time-varying networks, necessary and sufficient conditions for reaching average consensus is obtained from an algebraic perspective. Moreover, we show that if the integral network with period $T>0$ has a positive spanning tree over the time span $[0,T)$, average consensus for the node states is achieved. Simulation results are provided to demonstrate the theoretical analysis.

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arXiv2020

On the Controllability of Matrix-weighted Networks

This letter examines the controllability of consensus dynamics on matrix-weighed networks from a graph-theoretic perspective. Unlike the scalar-weighted networks, the rank of weight matrix introduces additional intricacies into characterizing the dimension of controllable subspace for such networks. Specifically, we investigate how the definiteness of weight matrices influences the dimension of the controllable subspace. In this direction, graph-theoretic characterizations of the lower and upper bounds on the dimension of the controllable subspace are provided by employing, respectively, distance partition and almost equitable partition of matrix-weighted networks. Furthermore, the structure of an uncontrollable input for such networks is examined. Examples are then provided to demonstrate the theoretical results.

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