Adaptive Protocol Design for Distributed Tracking with Relative Output Information: A Distributed Fixed-Time Observer Approach

This paper studies fully distributed adaptive protocol design for consensus tracking under leader-follower directed communication graphs, where only relative output information between neighboring agents is available. The main difficulty lies in the coupling between the structural constraint and the nonlinearity of the nominal controller, where the former is introduced by distributed observer design with only relative output information and the latter is due to adaptive gain to estimate the connectivity of the Laplacian matrix. To circumvent the aforementioned difficulty, we decouple it into two steps. First, the idea of an unknown input observer is introduced to propose the distributed observer, which can estimate the consensus error in fixed time. The fully distributed adaptive protocol is then generated by the proposed distributed observer to achieve consensus tracking. Both the full-order and reduced-order distributed fixed-time observers are proposed to form fully distributed adaptive protocols based on only relative output information, without using any eigenvalue information of the Laplacian matrix, or exchanged information of distributed observers between neighboring agents.