Yuanshi Zheng

Yuanshi Zheng, Jingying Ma, Long Wang

In this paper, we consider the consensus problem of hybrid multi-agent system. First, the hybrid multi-agent system is proposed which is composed of continuous-time and discrete-time dynamic agents. Then, three kinds of consensus protocols are presented for hybrid multi-agent system. The analysis tool developed in this paper is based on the matrix theory and graph theory. With different restrictions of the sampling period, some necessary and sufficient conditions are established for solving the consensus of hybrid multi-agent system. The consensus states are also obtained under different protocols. Finally, simulation examples are provided to demonstrate the effectiveness of our theoretical results.

Jiamin Wang, Jian Liu, Feng Xiao et al.

Understanding what governs collective robustness and how it can be enhanced remains a central pursuit in network science. This paper investigates the robustness of multi-agent consensus networks, quantified by the $H_2$ performance metric, and delves into the enhancing effect of agents' local memory on it. Inspired by the hierarchical temporal structure of memory observed in neuroscience, we focus on the role of memory depth, which reflects the temporal features of memory from recent to remote. Building on linear extrapolation, we propose a consensus protocol with single-step memory and tunable memory depth, derive the necessary and sufficient condition for achieving consensus, and show that the protocol exhibits an inheritable consensus property across memory depths. Furthermore, analytical expressions for the $H_2$ performance metric, which depend on the memory factor, memory depth, coupling gain, and Laplacian spectrum, are established. Under balanced usage of real-time and memory information, we demonstrate that memory at any accessible depth enhances $H_2$ performance, and the optimal memory depth occurs at either the most recent or the most remote memory, contingent upon certain parameter regions. Further detailed discussions are provided to clarify the broader implications of our findings.

Yuanshi Zheng, Jingying Ma, Long Wang

In this paper, we consider the consensus problem of switched multi-agent system composed of continuous-time and discrete-time subsystems. By combining the classical consensus protocols of continuous-time and discrete-time multi-agent systems, we propose a linear consensus protocol for switched multi-agent system. Based on the graph theory and Lyapunov theory, we prove that the consensus of switched multi-agent system is solvable under arbitrary switching with undirected connected graph, directed graph and switching topologies, respectively. Simulation examples are also provided to demonstrate the effectiveness of the theoretical results.

Xue Lin, Yuanshi Zheng, Long Wang

In this paper, a discrete-time multi-agent system is presented which is formulated in terms of the delta operator. The proposed multi-agent system can unify discrete-time and continuous-time multi-agent systems. In a multi-agent network, in practice, the communication among agents is acted upon by various factors. The communication network among faulty agents may cause link failures, which is modeled by randomly switching graphs. First, we show that the delta representation of discrete-time multi-agent system reaches consensus in mean (in probability and almost surely) if the expected graph is strongly connected. The results induce that the continuous-time multi-agent system with random networks can also reach consensus in the same sense. Second, the influence of faulty agents on consensus value is quantified under original network. By using matrix perturbation theory, the error bound is also presented in this paper. Finally, a simulation example is provided to demonstrate the effectiveness of our theoretical results.

Jing Qi, Yuxiang Wang, Zhiyuan Yu et al.

Continual Knowledge Graph Embedding (CKGE) aims to continually learn embeddings for new knowledge, i.e., entities and relations, while retaining previously acquired knowledge. Most existing CKGE methods mitigate catastrophic forgetting via regularization or replaying old knowledge. They conflate new and old knowledge of an entity within the same embedding space to seek a balance between them. However, entities inherently exhibit multi-faceted semantics that evolve dynamically as their relational contexts change over time. A shared embedding fails to capture and distinguish these temporal semantic variations, degrading lifelong link prediction accuracy across snapshots. To address this, we propose a Multi-Faceted CKGE framework (MF-CKGE) for semantic-aware link prediction. During offline learning, MF-CKGE separates temporal old and new knowledge into distinct embedding spaces to prevent knowledge entanglement and employs semantic decoupling to reduce semantic redundancy, thereby improving space efficiency. During online inference, MF-CKGE adaptively identifies semantically query-relevant entity embeddings by quantifying their semantic importance, reducing interference from query-irrelevant noise. Experiments on eight datasets show that MF-CKGE achieves an average (maximum) improvement of 1.7% (2.7%) and 1.4% (3.8%) in MRR and Hits@10, respectively, over the best baseline. Our source code and datasets are available at: https://anonymous.4open.science/r/MF-CKGE-04E5.

Qi Zhao, Shaoxuan Cui, Baolin Zhang et al.

Winner-take-all (WTA)--type selection is a fundamental mechanism in networked competition, yet its dependence on higher-order interactions remains insufficiently understood. We study a Lotka--Volterra competitive dynamics on higher-order networks, where classical pairwise inhibition is augmented by multi-way interaction terms induced by hyperedges of uniform hypergraphs. The proposed model shows multiple competitive outcomes, including WTA, winner-share-all (WSA), and variant winner-take-all (VWTA). The existence, uniqueness and stability of equilibria are rigorously proved through mathematical analysis, which relies on classical stability theory and recent advances in tensor algebra. We show that the eventual selection outcome is relatively insensitive to the hyperedge order and the specific higher-order coupling structure, and is instead determined by a small set of interpretable scalar parameters, such as the ratio between self-inhibition and lateral-inhibition and the external inputs. Numerical experiments support the theory by showing that higher-order interactions affect convergence and steady states, yet yield the similar outcome taxonomy (WTA/WSA/VWTA) as in standard graphs. These results provide a network-scientific explanation of the robustness of WTA-type outcomes under complex group interactions and offer principled guidance for designing selection mechanisms on higher-order networks.

Gangshan Jing, Yuanshi Zheng, Long Wang

In this paper, we study the consensus problem for continuous-time and discrete-time multi-agent systems in state-dependent switching networks. In each case, we first consider the networks with fixed connectivity, in which the communication between adjacent agents always exists but the influence could possibly become negligible if the transmission distance is long enough. It is obtained that consensus can be reached under a restriction of either the decaying rate of the transmission weight or the initial states of the agents. After then we investigate the networks with state-dependent connectivity, in which the information transmission between adjacent agents gradually vanishes if their distance exceeds a fixed range. In such networks, we prove that the realization of consensus requires the validity of some initial conditions. Finally, the conclusions are applied to models with the transmission law of C-S model, opinion dynamics and the rendezvous problem, the corresponding simulations are also presented.

Jingying Ma, Yuanshi Zheng, Bin Wu et al.

It is typical to assume that there is no conflict of interest among leaders. Under such assumption, it is known that, for a multi-agent system with two leaders, if the followers' interaction subgraph is undirected and connected, then followers will converge to a convex combination of two leaders' states with linear consensus protocol. In this paper, we introduce the conflict between leaders: by choosing k followers to connect with, every leader attempts all followers converge to himself closer than that of the other. By using graph theory and matrix theory, we formulate this conflict as a standard two-player zero-sum game and give some properties about it. It is noteworthy that the interaction graph here is generated from the conflict between leaders. Interestingly, we find that to find the optimal topology of the system is equivalent to solve a Nash equilibrium. Especially for the case of choosing one connected follower, the necessary and sufficient condition for an interaction graph to be the optimal one is given. Moreover, if followers' interaction graph is a circulant graph or a graph with a center node, then the system's optimal topology is obtained. Simulation examples are provided to validate the effectiveness of the theoretical results.