A fixed-time distributed extended state observer for uncertain second-order nonlinear system.

This paper investigates the fixed-time distributed estimation problem for a class of second-order nonlinear systems with uncertain input, unknown nonlinearity and matched perturbation. A fixed-time distributed extended state observer (FxTDESO) consisting of a group of local observer nodes under directed communication topology is proposed, and each node can reconstruct both the full state and unknown dynamics of the system. To achieve fixed-time stability, a Lyapunov function is elaborated, and based on this, sufficient conditions for the existence of the FxTDESO are established. Under time-invariant and time-varying disturbance, the observation errors can converge to the origin and a small region of the origin within a fixed time, respectively, where the upper bound of the settling time (UBST) is irrelevant to the initial conditions. Compared to the existing fixed-time distributed observers, the proposed observer can reconstruct both the unknown states and uncertain dynamics, and only the output of the leader and 1-dimensional output estimates from the neighboring nodes are needed in the observer design which effectively reduces the communication load. The paper also extends previous finite-time distributed extended state observer to the case of time-variant disturbance and eliminates the complex linear matrix equation assumption that guarantees the finite-time stability. Furthermore, the FxTDESO design for a class of high-order nonlinear systems is also discussed. Finally, simulation examples are conducted to demonstrate the effectiveness of the proposed observer. • A fixed-time distributed extended state observer (FxTDESO) containing a group of local observers is developed for an uncertain second-order nonlinear system. Each local observer can accurately reconstruct both the full state and lumped uncertainties in a fixed time. Compared to previous distributed extended state observers, the upper bound of the settling time of the observation errors is regardless of the initial conditions. • Unlike the existing fixed-time distributed observers which can only be used to estimate the system states and require the full state of the leader and full-state estimates from the observer nodes, both the states and uncertain dynamics can be reconstructed by our observer. Moreover, only output information of the leader and 1-dimensional output estimates of the local observer nodes are needed, which can effectively reduce the communication load. • When only the output information is available, it is challenging to find a way to analyze the fixed-time stability. To this end, a Lyapunov function is elaborated, and based on this, sufficient conditions for realizing fixed-time stability of the FxTDESO under time-invariant and time-varying disturbance are established, respectively. Furthermore, the FxTDESO design and stability analysis for a class of high-order nonlinear systems is briefly discussed. [ABSTRACT FROM AUTHOR]