Consensus of Hybrid Multi-agent Systems (1512.03189v1)

Abstract: 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.

• The paper develops necessary and sufficient conditions for achieving consensus in hybrid systems with continuous and discrete dynamics.
• It proposes and analyzes three distinct protocols, including a gossip-like approach ensuring mean square convergence under specific network conditions.
• Numerical simulations validate the theoretical findings, providing practical insights for applications in robotics, sensor networks, and automated traffic systems.

Consensus of Hybrid Multi-agent Systems

The paper "Consensus of Hybrid Multi-agent Systems" by Yuanshi Zheng, Jingying Ma, and Long Wang investigates the consensus problem within hybrid multi-agent systems. These systems are characterized by incorporating both continuous-time and discrete-time dynamic agents. The authors have proposed various consensus protocols with analytical tools primarily derived from matrix theory and graph theory. They developed necessary and sufficient conditions for achieving consensus and validated their theoretical results through numerical simulations.

The research explores three specific cases of consensus protocols tailored to hybrid multi-agent systems, describing distinct interaction environments. In the first case, the model stipulates that all agents communicate and update within a defined sampling period. Consensus is shown viable if and only if the underlying communication graph structure possesses a directed spanning tree. Moreover, for a sampling period $h < \frac{1}{\max_i \{ d_{ii} \}}$, the system can reach consensus, mirroring results well-known in homogeneous multi-agent systems.

The second case assumes continuous-time dynamic agents can observe their state in real-time, which relaxes the sampling period constraint to $h < \frac{1}{\max_{i \in I_n/I_m} \{ d_{ii} \}}$. Hybrid systems offer a rich field of paper due to their proximity to real-world applications, where discrete and continuous dynamics are often intertwined, yet the complexity increases due to their hybrid nature. Therefore, understanding their collective behavior under varied conditions holds significant importance.

In the third case, the authors present a gossip-like protocol under an undirected communication network. Here, hybrid agents engage in pair-wise communication based on probabilistic selection, and the network connectivity coupled with the condition $h < \frac{1}{\max_{i,j} \{ a_{ij} \}}$ is essential for convergence to consensus in a mean square sense. This approach is particularly useful for addressing consensus in scenarios where real-time communication is not feasible.

Importantly, the paper makes clear the challenges hybrid systems present, given the discrepancy in their operational timelines, yet navigates these issues through effective protocol design and analysis. The simulation results are consistent with the theoretical findings, clearly demonstrating the conditions under which consensus is achieved.

The implications of this research are noteworthy in both practical applications and theoretical frameworks. From a practical perspective, designing effective consensus algorithms for systems composed of heterogeneous agents (i.e., agents operating on different time scales) can be transformative for applications such as distributed robotics, sensor networks, and automated traffic systems. Theoretically, this work expands existing consensus theory by providing conditions and protocols adaptable to hybrid systems, potentially influencing future studies in consensus and coordination of multi-agent systems.

Looking ahead, further exploration into second-order consensus, time-delays, and their effects on hybrid systems could refine the applicability of these protocols. The increasing complexity of agents and networks—mirroring a more realistic setup—presents an enduring challenge but also elevates the significance of finding robust coordination mechanisms that this research significantly contributes to.