Distributed Adaptive Mittag–Leffler Formation Control for Second-Order Fractional Multi-Agent Systems via Event-Triggered Control Strategy

Abstract

This brief investigates the Mittag–Leffler formation bounded control problem for second-order fractional multi-agent systems (FMASs), where the dynamical nodes of followers are modeled to satisfy quadratic (QUAD) condition. Firstly, under the undirected communication topology, for the considered second-order nonlinear FMASs, a distributed event-triggered control scheme (ETCS) is designed to realize the global Mittag–Leffler bounded formation control goal. Secondly, by introducing adaptive weights into triggering condition and control protocol, an adaptive event-triggered formation protocol is presented to achieve the global Mittag–Leffler bounded formation. Thirdly, a five-step algorithm is provided to describe protocol execution steps. Finally, two simulation examples are given to verify the effectiveness of the proposed schemes.

Leader-Following Formation Control for Discrete-Time Fractional Stochastic Multi-Agent Systems by Event-Triggered Strategy

“…By extending fractional dynamics to multi-agent systems, the formation control challenge in fractional multi-agent systems has emerged as a captivating and sought-after research area. Unlike conventional integer-order systems, fractional-order dynamics introduce memory effects and long-range interactions among agents, allowing for more sophisticated and nuanced formation control strategies [15][16][17]. Various control techniques have been employed and refined in the realm of fractional formation control, such as sliding-mode control [18,19], double-integrator control [20], and both-and-observer control [21].…”

Iterative Learning Formation Control via Input Sharing for Fractional-Order Singular Multi-Agent Systems with Local Lipschitz Nonlinearity

“…In recent years, communication and coordination between multi-agent systems (MASs) have become more significant means to improve the efficiency and performance of solving large-scale complex problems, such as the cooperative control problem of MASs (including formation control [1], containment control [2,3], etc.). In [1], for the considered secondorder nonlinear FMASs, an adaptive event-triggered formation protocol is presented to achieve the global Mittag-Leffler bounded formation. The issue of fixed-time output event-triggered containment control for a class of second-order nonlinear MASs with Markov switching topology is investigated in [2].…”

“…f (x k,i (t), x k,i (t − h), t) is a continuous nonlinear time-delay term. The other parameter definitions are the same as Equation(1). For the nonlinear time-delay FOSMASs under the D α -type iterative learning protocol with input sharing scheme and if Assumptions 1-3 are met, if there exists a learning gain that satisfies…”