A Predictor-Based Approach to Communication Delay Compensation for Multi-Agent Systems

In this paper, we propose a novel predictor-based communication delay compensation method in the stabilization problem of multi-agent systems. The known constant communication delays exist between the agents, but there is no input delay in each agent's dynamics. The dynamics of agents can be heterogeneous, but they are linear, and there is no physical interaction among them. Each agent is assumed to know the other agents' dynamics, i.e., the state equation of the other agents. For these systems, we propose a prediction method for other agents' states. The concept of the proposed approach is trust in a unique fiction; each agent assumes that "the other agents can precisely predict the current states of the whole system and move as if there is no communication delay." It is demonstrated that, under the proposed method, this assumption holds inductively if it is valid for a certain time interval. To ensure the validity of this assumption, we also propose a mechanism for synchronizing the start timing of predictions, establishing an initial condition for the system. The stability of the proposed method is rigorously analyzed using the Lyapunov condition and the linear matrix inequality (LMI) condition. Under the LMI condition, the above synchronization mechanism is not essential. The effectiveness of the proposed method is verified with numerical simulations (with and without disturbance). In the absence of disturbance, the performance recovers to the quite similar performance as if there were no delay. Even in the presence of disturbance, the system remains highly stable. In addition, we provide context on the communication delays in multi-agent systems, and we explicitly highlight the unique contributions of our method compared to existing approaches.