Coordination of multi‐agent systems with arbitrary convergence time

Abstract

This paper proposes fixed‐time solutions to several problems in multi‐agent systems. First, a fixed‐time consensus protocol is investigated and under the assumption that the lower bound of smallest positive eigenvalue of the Laplacian matrix is known in advance, the consensus time of the protocol can be arbitrarily selected. Second, the consensus law to attenuate bounded disturbances acting on the system is modified. Third, the fixed‐time design method is applied to the orientation alignment and network localization problems. Finally, several simulations are provided to support the mathematical analysis.

Compensator-based periodically intermittent control for nonlinear second-order multi-agent systems

“…Thus, more and more researchers have focused on nonlinear multi-agent systems in recent years. 8–12 In the work of Zhang et al, 8 the second-order nonlinear multi-agent systems with time-varying delays communication networks were investigated. In the work of Mao et al, 9 the reduced-order observers were designed to deal with the leader-following consensus problem of second-order nonlinear multi-agent systems with uncertain control coefficient.…”

“…The high-order nonlinear multi-agent systems with input delays were studied in the recent researches. 10,11 A lot of nonlinear multi-agent systems contain both first-order systems and second-order systems, which are called nonlinear heterogeneous multi-agent systems, and the cooperative control problem of nonlinear heterogeneous multi-agent systems was studied by Du et al 12…”

“…As an important part of the research of multi-agent systems, cooperative control of multi-agent systems has attracted considerable attentions. The research on cooperative control can be divided into consensus control, 11,13 bipartite consensus control, 14,15 formation control, 16,17 flocking control 18,19 and so on. In order to select the convergence time of multi-agent systems, Nguyen et al 11 proposed a class of fixed-time solutions for nonlinear multi-agent systems, and generalized the methodology the researches of orientation alignment and bearing-based network localization.…”

“…The research on cooperative control can be divided into consensus control, 11,13 bipartite consensus control, 14,15 formation control, 16,17 flocking control 18,19 and so on. In order to select the convergence time of multi-agent systems, Nguyen et al 11 proposed a class of fixed-time solutions for nonlinear multi-agent systems, and generalized the methodology the researches of orientation alignment and bearing-based network localization. The leader-following consensus problem for nonlinear multi-agent systems was investigated in the work of Ménard et al, 13 and the exponential practical convergence was guaranteed by the proposed control protocol.…”

Free-Will Arbitrary Time Consensus Protocols with Diffusive Coupling

“…An extension of [5] to prespecified time bearing-only formation control is given in [13]. Recently, free-will arbitrary time (FwAT) consensus protocols, built upon the results in [14], are presented in [1], [15]. In FwAT consensus, the settling time is bounded by a preset finite time t f , which does not depend on the initial condition nor any system parameter.…”