Fully distributed practical bipartite formation tracking of networked Lagrangian systems with actuator faults and bounded inputs

Abstract

This paper investigates the bipartite formation tracking (BFT) problem of networked Lagrangian systems (NLSs) with signed directed graphs. Each system suffers from actuator fault with bounded input. Firstly, the unknown input of the leader is estimated for all the followers based on an observer in the prescribed time, which is constructed by employing a time base generator (TBG). Then, a hierarchical fully distributed controller is proposed to achieve BFT without using the global information with respect to the communication graphs. Then, the related sufficient condition for the system stability is derived by means of the Lyapunov theory. Finally, a simulation example is proposed to demonstrate the performance of the hierarchical fully distributed controller for achieving BFT.

Keywords:

• Bipartite formation tracking (BFT)
• networked Lagrangian systems (NLSs)
• hierarchical fully distributed controller
• signed digraphs

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China under Grant 62073301 and Grant 61503282, in part by the National Key Technology R&D Program of China under Grant 2020YFB1709301 and Grant 2020YFB1709304, in part by the Natural Science Foundation of Hubei Province of China under Grant 2021CFB516, in part by the Innovative Development Project for Supporting Enterprise Technology of Hubei Province of China under Grant 2021BAB094, in part by the Fundamental Research Funds for the Central Universities (WUT: 2021III062JC)，and the open project of Key Laboratory of Image Processing and Intelligent Control (Huazhong University of Science and Technology), Ministry of Education.