Robust consensus of nonlinear multi‐agent systems via reliable control with probabilistic time delay

Abstract

In this paper, the consensus problem of uncertain nonlinear multi-agent systems is investigated via reliable control in the presence of probabilistic time-varying delay. First, the communication topology among the agents is assumed to be directed and fixed. Second, by introducing a stochastic variable which satisfies Bernoulli distribution, the information of probabilistic time-varying delay is equivalently transformed into the deterministic time-varying delay with stochastic parameters. Third, by using Laplacian matrix properties, the consensus problem is converted into the conventional stability problem of the closed-loop system. The main objective of this paper is to design a state feedback reliable controller such that for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop system is robustly stable in the sense of mean-square. For this purpose, through construction of a suitable Lyapunov-Krasovskii functional containing four integral terms and utilization of Kronecker product properties along with the matrix inequality techniques, a new set of delay-dependent consensus stabilizability conditions for the closed-loop system is obtained. Based on these conditions, the desired reliable controller is designed in terms of linear matrix inequalities which can be easily solved by using any of the effective optimization algorithms. Moreover, a numerical example and its simulations are included to demonstrate the feasibility and effectiveness of the proposed control design scheme.

Leader‐following consensus of nonlinear singular multiagent systems with intermittent communication

“…Remark In practice, time‐varying delay or randomly occurring time delay often exists in the communication channel (see the works of Kaviarasan et al and Sakthivel et al), and the dynamics of each agent may not be identical (see the work of Ma). Therefore, extending the present work to the more general cases where communication time delay exists or agents are heterogeneous is an interesting issue to be studied in the future.…”

“…A common thread of consensus research is that a group of agents try to achieve a collective behavior or global coordination by using the neighborhood information. Generally speaking, consensus research is classified into leaderless consensus [1][2][3][4][5][6][7][8][9] and leader-following consensus. [9][10][11][12][13][14][15] Many dynamic models have been extensively studied for the consensus problem, such as first-order integrator, [1][2][3]11 second-order integrator, 4,5,11,14 general linear, 9,10,12,13 and nonlinear dynamics.…”

“…[9][10][11][12][13][14][15] Many dynamic models have been extensively studied for the consensus problem, such as first-order integrator, [1][2][3]11 second-order integrator, 4,5,11,14 general linear, 9,10,12,13 and nonlinear dynamics. 7,8,15 Recently, consensus of MASs with singular dynamics has also been concerned.…”

Event‐Triggered Consensus Control for Leader‐Following Multiagent Systems Using Output Feedback

“…Consensus is a basic problem in the cooperative control of multiagent systems [1][2][3][4][5], which is generally realized through the behavior-based method or the leader-following approach. To be specific, the leader-following consensus problem has been studied in [6][7][8][9][10][11][12] from different perspectives, where all the following agents can reach consensus by tracking a real or virtual leader based on local interactions.…”

“…Then x i t can asymptotically reach x 0 t by x i t = x i t − h i t and x 0 t = x 0 t − h 0 t . Therefore, the consensus of leader-following multiagent systems (1) and (2) is reformulated as the asymptotical stability problem of system (17). In other words, if (17) is asymptotically stable at the origin, then the multiple agents reach consensus.…”