Observer‐based prescribed‐time consensus control for heterogeneous multi‐agent systems under directed graphs

Abstract

This work studies the prescribed‐time robust consensus tracking problem of heterogeneous multi‐agent systems over directed graphs. Aiming at multi‐agent systems with a static leader and only matched disturbances, a distributed observer‐based consensus algorithm is developed, to ensure that the tracking errors converge to zero accurately in prescribed time. For the case of multi‐agent systems with a dynamic leader and mismatched/matched disturbances, an adaptive strategy based on a distributed observer and a disturbance observer is designed by the dynamic damping reciprocal technology. Such strategy can avoid the numerical singularity, adapt to the situation that the upper bounds of the disturbances are unknown, and assure that the tracking errors converge to an adjustable neighborhood of zero within prescribed time. Finally, simulations are given to verify the effectiveness of the proposed control strategies.

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

“…However, some bottlenecks 14 still cannot be broken by finite-time/fixed-time distributed observers: (1) there exists a complex relationship between the upper bound of the settling time and observer design parameters; (2) the actual settling time heavily depends on the observer design parameters and the initial system conditions, and cannot be predefined in advance according to the task requirements. To overcome the bottlenecks, some efforts have been put into predefined-time distributed observers, [15][16][17][18][19][20][21] where the upper bound of the settling time is preset by only one parameter irrelevant to the initial conditions and other system parameters. For example, a predefined-time distributed observer 21 was proposed for a class of strict-feedback nonlinear systems.…”

“…It should be noted that the communication topology is global information (which is reflected as the Laplacian matrix) that is not easily accessible in multi-agent systems. Nevertheless, the designs of most existing distributed observers including predefined-time distributed observers [15][16][17][18][19][20][21] require the information of the communication graph, hindering the practical applications. Recently, a few fully distributed observers [22][23][24] to avoid using the Laplacian matrix information have been developed, which are mainly inspired by early works [25][26][27] of adaptive distributed consensus protocol design.…”

“…Hence, the nonlinearities of the leader system are needed by each follower to improve the cooperative control performance. Nonetheless, almost all the existing predefined-time distributed observers [15][16][17][18][19][20] are not suitable for the leader system with unknown system parameters and cannot be applied to estimating the nonlinearities.…”

“…3. Compare to the existing predefined-time distributed observers, [15][16][17][18][19][20][21] the proposed FPTDOs do not require any information of the Laplacian matrix. Moreover, unlike results 21,24 for strict-feedback nonlinear systems, the exact models of the nonlinear functions are not required by each follower in our article.…”

“…When the system parameters and the upper bounds of the leader's nonlinearities are available to each follower, an FPTDO is proposed to reconstruct the states of the leader within a predefined time irrelevant to the initial conditions. When the time‐varying system parameters and nonlinear functions of the leader are unavailable to each follower, an FPTDO is developed and is able to reconstruct the system parameters, nonlinearities and full state of the leader within a predefined time. In contrast to adaptive distributed observers, 4,28‐30 the time‐varying system parameters are considered. Compare to the existing predefined‐time distributed observers, 15‐21 the proposed FPTDOs do not require any information of the Laplacian matrix. Moreover, unlike results 21,24 for strict‐feedback nonlinear systems, the exact models of the nonlinear functions are not required by each follower in our article. …”