Consensus of Fractional-Order Multiagent Systems with Double Integral and Time Delay

Abstract

This paper is devoted to the consensus problems for a fractional-order multiagent system (FOMAS) with double integral and time delay, the dynamics of which are double-integrator fractional-order model, where there are two state variables in each agent. The consensus problems are investigated for two types of the double-integrator FOMAS with time delay: the double-integrator FOMAS with time delay whose network topology is undirected topology and the double-integrator FOMAS with time delay whose network topology is directed topology with a spanning tree in this paper. Based on graph theory, Laplace transform, and frequency-domain theory of the fractional-order operator, two maximum tolerable delays are obtained to ensure that the two types of the doubleintegrator FOMAS with time delay can asymptotically reach consensus. Furthermore, it is proven that the results are also suitable for integer-order dynamical model. Finally, the relationship between the speed of convergence and time delay is revealed, and simulation results are presented as a proof of concept.

Consensus Tracking of Fractional‐Order Multiagent Systems via Fractional‐Order Iterative Learning Control

“…e necessary and su cient conditions of FOMASs for containment control were presented in [15]. For FOMASs, several consensus problems of FOMASs were studied in [16][17][18][19]. Du et al studied the problem of robust consensus for second-order MASs and proposed a class of novel continuous nonsmooth consensus algorithms [20].…”

“…en, the matrix − (L + D) is the Hurwitz stable matrix. Accordingly, the gain matrix Γ D can be found to satisfy the condition in equation (17).…”

Consensus of Multi‐Integral Fractional‐Order Multiagent Systems with Nonuniform Time‐Delays

“…Meanwhile, by means of matrix theory tool, Laplace transform and graph theory tool, two delay margins were obtained as the consensus conditions. Lately, consensus of FOMASs with double integral was proposed in [35][36][37][38][39]. The consensus problem of FOMASs with double integral over fixed topology was studied in [35].…”

“…Based on the sliding mode estimator, consensus problem for FOMASs with double integral was studied in [37]. By means of matrix theory tool, Laplace transform, and graph theory tool, consensus problems for a FOMAS with double integral and time-delay were studied in [38]. Nevertheless, the above research results on the consensus problems of FOMASs with or without time-delays were based on the single-integral fractionalorder or double-integral fractional-order dynamics.…”

“…As far as we know, this paper is the first paper that studies consensus of MIFOMASs. Just as integer-order MASs have first-order (single-integral) MASs [4][5][6][7][8][9][10][11], second-order (double-integral) MASs [12][13][14][15][16], and high-order (multiintegral) MASs [17][18][19][20][21], FOMASs also have single-integral FOMASs [29][30][31][32][33][34], double-integral FOMASs [35][36][37][38][39], and MIFOMASs, which makes the overall theory of FOMASs perfect from single-integral to multi-integral FOMASs. In addition, single-integral and double-integral FOMASs are the special cases of MIFOMASs.…”