Robust finite-time consensus subject to unknown communication time delays based on delay-dependent criteria

Maryam Sharifi

doi:10.1177/01423312211051507

Abstract

In this paper, robust finite-time consensus of a group of nonlinear multi-agent systems in the presence of communication time delays is considered. In particular, appropriate delay-dependent strategies which are less conservative are suggested. Sufficient conditions for finite-time consensus in the presence of deterministic and stochastic disturbances are presented. The communication delays don’t need to be time invariant, uniform, symmetric, or even known. The only required condition is that all delays satisfy a known upper bound. The consensus algorithm is appropriate for agents with partial access to neighbor agents’ signals. The Lyapunov–Razumikhin theorem for finite-time convergence is used to prove the results. Simulation results on a group of mobile robot manipulators as the agents of the system are presented.

Highlights

Distributed cooperative control of multi-agent systems has been extensively studied in recent decades due to its applicability in the real physical world
Where r(t) = 1⁄2r1(t), :::, rN (t) is a vector Wiener process and H(X ) is a bounded matrix. This model considers a generic coupling with the disturbance and provides a sufficiently general and real representation for the system, which can include the interconnected network systems subject to stochastic couplings
In order to compensate for the adverse effects of time-delays and uncertainties in a finite-time interval, novel delay-dependent consensus algorithms have been suggested

Summary

Introduction

Distributed cooperative control of multi-agent systems has been extensively studied in recent decades due to its applicability in the real physical world. (1) Design of new distributed control algorithms to guarantee finite-time robust consensus in the presence of communication time-delays and disturbances Both deterministic and stochastic disturbances are considered and appropriate strategies are presented. 1. Utilizing the control algorithm of equation (10), H‘ finite-time consensus (Definition 2) in the presence of communication time-delays is achieved if there exist a matrix Q ø 0 and positive scalars a, b, such that that the following inequalities hold (M In)G(X )G(X )T(M In)T ł Q q = l++ma(axgh222aÀaaaÀÀ1)1À11lllmmmianax(x(P(PQ))21)2a1ÀaÀÀ+aÀ1a1(Rb22+1⁄2dn(RN1⁄2nTÀ()N+1À)aaÀ1Àa11)S+aTÀa1S1+i\10. Ef (t) is defined the same as equation (6) By this definition and considering the same control signal for the follower agents as equation (10), the dynamics of each parts of the new consensus error vector is achieved as e_ l (t).

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Conclusion