Hierarchical Decomposition Based Consensus Tracking for Uncertain Interconnected Systems via Distributed Adaptive Output Feedback Control

In this note, distributed adaptive controllers are developed for output consensus tracking of multiple linear systems with unknown parameters, uncertain subsystem interconnections and external disturbances. The subsystems are allowed to have non-identical dynamics and the same yet arbitrary order. It is assumed that only part of subsystems can have direct access to the time-varying trajectory information and the subsystem states are unmeasurable for local feedback control. In our design, the directed graph representing the information transmission status among subsystems is preprocessed by splitting it into a hierarchical structure. Then local adaptive controllers of subsystems in different layers can be computed in a sequential order and the difficulty on deriving mutually dependent local controls in previous consensus works are successfully overcome. In each subsystem, additional estimates are introduced to account for the unknown parameters and states in its neighbors' dynamics. Besides, only the information of local outputs and inputs need be collected from the neighboring subsystems. Certain robust terms are added in distributed adaptive laws to mitigate the effects of uncertain subsystem interactions and disturbances. It is proved that with our scheme, all closed-loop signals can be ensured bounded when the strengths of uncertain subsystem interconnections are sufficiently weak. The tracking errors for the entire group of subsystems will converge to a compact set and the transient tracking error performance can be adjusted by appropriately choosing design parameters.