Distributed Consensus of Multiple Euler–Lagrange Systems Networked by Sampled-Data Information With Transmission Delays and Data Packet Dropouts

In this paper, the distributed consensus problem for a class of multiple Euler-Lagrange systems is solved. The considered issues are: 1) sampled-data information; 2) transmission delay; and 3) data packet dropouts. The considered mathematical models can describe a large number of practical systems in the actual engineering. In particular, all of the information exchanges are modeled by a sample-and-hold mechanism, which is more reliable and practical in applications. Moreover, this framework can deal with time-varying transmission delays and data packet dropouts by taking into account the limited communication capacity of information exchanges. By utilizing model transformation and applying the Lyapunov-Krasovskii functional method, sufficient conditions are first established with single-packet information exchanges to ensure that the networked Euler-Lagrange systems can achieve consensus under undirected communication topology. Then, the obtained results are further extended to the multiple-packet transmission case. Finally, an example of four two-link manipulators with time-varying transmission delays and data packet dropouts is addressed to verify the effectiveness and applicability of our theoretical results.Note to Practitioners-The motivation of this paper is to investigate a practical networking strategy for the cooperative control of multiple Euler-Lagrange systems that have been widely applied in modeling robotic manipulators, autonomous underwater vehicles, and spacecrafts. Existing approaches are mainly based on the continuous-time communication network, which are difficult to be implemented in the real-world applications. In addition, energy consumption problems for multi-agent systems have received increasing attention in recent years, which also motivate us to carry out the present study. Since continuous-time communications inevitably consume much energy, how to find an effective way to reduce energy cost is an urgent task. Therefore, this paper presents a novel method for communications among multiple Euler-Lagrange systems based on the sampled-data information, where discrete-time communications are used instead of continuous-time communications. Another advantage of the proposed method is that it can significantly reduce the transmission energy consumption. Furthermore, both transmission delays and data packet dropouts are taken into account which make our results more applicable in practice.