Fully predefined‐time distributed observer design for second‐order strict‐feedback nonlinear systems

Abstract Distributed observer is an effective tool to deal with leader‐following control problems. This article investigates the fully predefined‐time distributed observer (FPTDO) design problem of a generalized second‐order strict‐feedback nonlinear leader system. Firstly, given the system parameters and the upper bounds of the system nonlinearities, an FPTDO is proposed to provide the state estimates. Secondly, considering that the time‐varying system parameters and nonlinear functions of the leader system are unknown to each follower, an FPTDO is developed to estimate the time‐varying system parameters, nonlinearities and full state of the leader. The proposed FPTDOs exhibit the following advantages: (1) the observation errors converge to zero within a finite time that is predefined by only one design parameter independent of the initial conditions; (2) the designs of the FPTDOs do not require any information of the communication topology (Laplacian matrix); and (3) the exact models of the nonlinear functions are not required by each follower. Finally, simulation examples are given to demonstrate the effectiveness of the proposed FPTDOs.