A hybrid systems approach to global synchronization and coordination of multi-agent sampled-data systems*

A global synchronization algorithm for a network of resetting clocks is presented. Each clock signals its neighbors when it resets to zero after reaching the end of its period. Based on where a neighbor is located at the time of the signal, the neighboring clock adjusts its value instantaneously to synchronize with the signaling clock. Subsequently, the sychronization algorithm is used in the context of networked, multi-agent sampled-data systems. Here, agents update their internal state, based on the values of the internal states of their neighbors, when their clock variable resets to zero. The synchronization algorithm, together with additional sampling of the internal states of neighbors, is used to synchronize and coordinate the agents of the networked sampled-data system. These actions enable achieving the stability property that would result if the agents performed their state updates simultaneously. The models associated with these algorithms are presented in terms of hybrid dynamical systems. Well-posed models are developed that exhibit robustness properties, including robustness to small communication delays and to small mismatch in the natural frequency of each clock, and for which extensive analysis tools are available, including an invariance principle and a reduction principle.