Consensus tracking problem for linear fractional multi-agent systems with initial state error

Abstract

In this paper, we discuss the consensus tracking problem by introducing two iterative learning control (ILC) protocols (namely, Dα-type and PDα-type) with initial state error for fractional-order homogenous and heterogenous multi-agent systems (MASs), respectively. The initial state of each agent is fixed at the same position away from the desired one for iterations. For both homogenous and heterogenous MASs, the Dα-type ILC rule is first designed and analyzed, and the asymptotical convergence property is carefully derived. Then, an additional P-type component is added to formulate a PDα-type ILC rule, which also guarantees the asymptotical consensus performance. Moreover, it turns out that the PDα-type ILC rule can further adjust the final performance. Two numerical examples are provided to verify the theoretical results.

Iterative learning control for impulsive multi-agent systems with varying trial lengths

“…Since ν > 0, then the number of times L i+1 takes the value G, which is also infinite times. By ( 6), (21), and ( 13) we have lim i→∞ ψ * i+1 λ = 0. The proof is completed.…”

“…• Fractional iterative learning laws has a memory function and keeps the global information fully, which can be used to improve the learning effect. Recently, Luo et al [20,21] studied the fractional ILC problem of fractional multi-agent systems. Liu et al [15][16][17] studied the ILC of VTL for fractional impulsive systems.…”

Bounded consensus of double-integrator stochastic multi-agent systems

“…Furthermore, ´ ı ∈ R is the noise intensity, ı (t) is the standard white noise. Concerning on the fractional multi-agent systems, we can still obtain the corresponding bounded consensus condition, see [28,29,30].…”

Consensus of nonlinear multiagent systems with uncertain disturbance under stochastic switching topologies

“…Consensus problem, the hottest research topic about the multiagent systems, is first formulated and studied in Jadbabaie et al 3 and Olfati‐Saber and Murray 4 . Subsequently, a emerging research subject has attracted wide attention from researchers, for instance, formation problems, 5 learning control problems, 6,7 and fractional consensus 8,9 . This is because there exist a large amount of group dynamical behaviors which can be modeled as a complex network.…”

“…4 Subsequently, a emerging research subject has attracted wide attention from researchers, for instance, formation problems, 5 learning control problems, 6,7 and fractional consensus. 8,9 This is because there exist a large amount of group dynamical behaviors which can be modeled as a complex network. The researchers make effort to design a variety of control protocols to regulate the global dynamical behaviors of the agents for some objectives, for example, impulsive control, 10 containment control, 11 and optimization control.…”