Observer‐based leaderless and leader‐following consensus for multiagent systems: A modified integral‐type event‐triggered design

Abstract

SummaryThis article aims to solve leaderless and leader‐following consensus problems for general linear systems by integral‐type event‐triggered control method. Different from the existing integral‐type event‐triggered controllers for multiagent systems (MASs), a modified distributed integral‐type event‐triggered scheme is designed via defining a measurement error without continuous communication. Then, distributed event‐triggered protocols are proposed for MASs to achieve the leaderless and leader‐following consensus. Moreover, for the case that all the agents' states are not available, distributed observers are given to estimate the full states. Meanwhile, leaderless and leader‐following consensus problems are investigated based on the observer‐based event‐triggered schemes. In addition, no agent will exhibit Zeno behavior. Finally, simulations are given to verify the effectiveness of our results.

Event‐triggered bipartite consensus for multiagent systems with general linear dynamics: An integral‐type event‐triggered control

“…The idea of integral‐based event‐triggering condition yielding larger inter‐event intervals was proposed by Mousavi, Ghodrat and Marquez 36 . Later, this idea is applied to MASs in 37 and it has been investigated further in References 38–41. In particular, Zhang, Lunze and Wang 39 showed that the proposed controller system for the consensus problem has a positive MIET and the consensus is achieved asymptotically without a small error.…”

“…In particular, Zhang, Lunze and Wang 39 showed that the proposed controller system for the consensus problem has a positive MIET and the consensus is achieved asymptotically without a small error. However, there is a gap in the proofs of the consensus for the system in References 38–41 as they applied Barbalat's lemma without proving the uniform boundedness of the derivative of the consensus test function $$$ \delta (t) $$$ which is a nontrivial step. To overcome this gap, Ma and Zhao 42 put an extra condition about the boundedness of measurement error functions inside their proposed integral‐based event‐triggering protocol.…”

“…Statement of contributions : We design a new integral‐based event‐triggered control for the bipartite consensus of general linear MASs and hence fill a gap in the proofs in the previous works 38–41 for the consensus problems using the integral‐based event‐triggered controls. Our proposed protocol is even better than the integral‐based event‐triggered control introduced in 42 as we do not need any assumption of uniformly boundedness of $$$ e(t) $$$, the error measurement function of the system, as 42 added.…”

Event-triggered bipartite consensus for multiagent system with general linear dynamics: an integral-type event triggered control

“…The idea of integral-based event-triggering condition yielding larger inter-event intervals was proposed by Mousavi, Ghodrat and Marquez [34]. Later, this idea is applied to multiagent systems in [35] and it has been investigated further in [36], [37], [23], [38], [39]. In particular, Zhang, Lunze and Wang [38] showed that the proposed controller system for the consensus problem has a positive MIET and the consensus is achieved asymptotically without a small error.…”

“…One essential step in proving the consensus using integral based eventtriggered control is the application of Barbalat's lemma. This step requires obtaining a uniform bound for the derivative V of the a Lyapunov function V used in the proof ( [36], [37], [38], [23], [39]). We give a full detail for obtaining the uniform boundedness of the derivative (Lemma III.4).…”