Bipartite Tracking Consensus for High-Order Heterogeneous Uncertain Nonlinear Multi-Agent Systems With Unknown Leader Dynamics via Adaptive Fully-Distributed PID Control

This article tackles the problem of bipartite tracking consensus for high-order heterogeneous nonlinear and uncertain Multi-Agent Systems (MASs) interacting over directed signed graphs, where the agent nonlinear dynamics, including the leader ones, are general and unknown. A novel fully-distributed adaptive PID-like protocol, that does not require any prior knowledge about the global information of the network structure and/or any distributed observer for leader dynamics estimation, is proposed to solve the problem. Based on the Lyapunov theory, we derive adaptive mechanisms able to guarantee the robust asymptotic convergence of the overall networked system and the boundedness of the time-varying control signals. To achieve these control objectives, the computation of the adaptive control actions leverages only a limited amount of time-varying information, thus preserving the communication channel bandwidth and reducing the computational burden required at the single agent level. A numerical analysis supports the theoretical derivation.