Theory and Experiment on Nonlinear Distributed Observer Design for Prescribed-Time Output Formation Tracking of Heterogeneous Nonlinear Networks

This paper presents a distributed observer-based non-linear control framework to address a prescribed-time output formation tracking problem of heterogeneous nonlinear networks under a nonlinear leader system and a digraph with a spanning tree, wherein dynamics and dimensions of leader-follower systems can be different. To solve this issue, prescribed-time nonlinear distributed observers are firstly developed to estimate the nonlinear leader’s state, and the prescribed-time distributed control law is further presented. Under this framework, the zero-error output formation tracking is obtained within a pre-specified and user-defined time by leveraging the time transformation approach. The proposed algorithm is free of global knowledge, and its convergence time is irrelevant to initial conditions, control parameters or network structures. Simulation and experimental results are given to verify the designs’ effectiveness. The main features of developed designs lie in that: (1) prescribed-time output formation tracking of heterogeneous nonlinear systems can be achieved under directed graphs, wherein both dynamics and dimensions of leader-follower nonlinear systems can be different; (2) the convergence time is pre-specified and thus, irrelevant to any initial conditions, control parameters, or network structures; (3) the proposed algorithm that does not depend on any global information, is distributed under a general communication graph with a directed spanning tree; and (4) the prescribed-time output formation tracking solution can be extended beyond the terminal time.