Distributed Control under Transmission Delays: A Model-Based Hybrid System Approach

Networked systems, in practice, suffer from several network-induced imperfections. In this paper, we consider the problem of distributed control of nonlinear multi-agent systems (MASs) where the information broadcasts over a network are susceptible to one such imperfection, namely, transmission delays. The design methodology employed is such that the sampling instants (at which agents broadcast information) could be both aperiodic and asynchronous in nature. The broadcasts, upon arrival, are propagated by the agents through dynamical models and these propagates are used in their control protocols. The overall MAS is formulated as a hybrid dynamical system whose stability governs the upper bounds on: a) the sampling interval, namely, the duration between two consecutive broadcasts, and b) the transmission delays that the broadcasts might be prone to. Finally, through a case study on the consensus of Lipschitz nonlinear agents, we demonstrate the effectiveness of the proposed methodology.