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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.

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