Edge-Based Self-Triggering Impulsive Consensus on Nonlinear Multi-Agent Systems With Proportional Delay

This paper investigates the cosensus for a class of nonlinear multi-agent systems. As one of the boundless delays, proportional delay is introduced by considering the existence of tremendous amount of parallel information transfer paths with different axon sizes or lengths. To better reduce the complexity of analysis, three different parameter functions are constructed to deal with the proportional delayed systems. In view of the limited bandwidth and fully distributed architecture of agents in most practical applications, the distributed edge-based self-triggering impulsive (DEBSTI) controller is elaborately designed to eliminate the continuous monitoring, high control costs and global information transmission. Sufficient conditions are derived for achieving the consensus globally and exponentially by utilizing the methods of parameter variation, comparison principle, and average impulsive interval. In addition, the Zeno behavior could be avoided. Furthermore, a larger value range for the impulsive-effect-related parameter taking is obtained by considering the diverse functions of the impulses. Correspondingly, different convergence rates based on different ranges are calculated precisely. Finally, twenty one-link manipulators actuated by twenty DC motors are discussed in numerical simulation to demonstrate the effectiveness of the proposed results.
Note to Practitioners
—Nonlinear multi-agent systems could be applied to simulate large-scale systems like UAV formation and one-link manipulator with revolute joints. By considering the continuous monitoring, high control costs and global information transmission, the DEBSTI controller is skillfully designed. In view of the tremendous amount of parallel information transfer paths with different axon sizes or lengths, the proportional delay is taken into consideration to make results more practical based on three different parameter functions. Moreover, different impulsive functions are discussed. In numerical simulation, the one-link manipulator with revolute joints actuated by a DC motor is modeled to reflect the industrial application scenarios.