Impulsive practical tracking synchronization of networked uncertain Lagrangian systems without and with time-delays

This paper presents a procedure for studying tracking synchronization of networked Lagrangian systems via impulsive control, where each agent is allowed to be nonidentical, even uncertain dynamics. Some algebraic criteria for tracking synchronization without and with time-delays are established respectively. It turns out that these criteria can provide a novel impulsive control strategy to synchronize globally networked Lagrangian systems to a given time-varying target trajectory with a desired tracking error bound (called as practical tracking synchronization). A distinctive feature of the developed control strategy is fully to take into account the effects of impulsive constraints, and thereby to yield impulsive synchronization motion of networked Lagrangian systems, provided that each agent instantaneously interacts with its neighbors only at some discrete moments. As a direct application of the theoretical results, practical tracking synchronization of nonidentical 3-DOF mobile robots without and with time-delays is discussed in detail. Simulation results illustrate and visualize the effectiveness and feasibility of the proposed control technique.