Effects of Delay in Multi-Agent Consensus and Oscillator Synchronization

Abstract

The coordinated motion of multi-agent systems and oscillator synchronization are two important examples of networked control systems. In this paper, we consider what effect multiple, noncommensurate (heterogeneous) communication delays can have on the consensus properties of large-scale multi-agent systems endowed with nonlinear dynamics. We show that the structure of the delayed dynamics allows functionality to be retained for arbitrary communication delays, even for switching topologies under certain connectivity conditions. The results are extended to the related problem of oscillator synchronization.

Distributed Consensus of Nonlinear Multi-Agent Systems on State-Controlled Switching Topologies

“…Based on algebraic graph theory, Olfati-Saber and Murray [1] discussed the consensus problem for networked single-integrator agents over directed fixed and switching topologies with communication time-delays. Following this work, the consensus problem has been recently investigated from various perspectives, for example, system with second-order dynamics [8,9], nonlinear agent dynamics [10,11], time-delays [12,13], quantization [14], saturation [15], etc. However, most of the aforementioned works were predominantly concerned with the multi-agent systems under fixed communication topologies.…”

LQR performance for multi-agent systems: Benefits of introducing delayed inter-agent measurements

“…Significant research efforts analyzing stability and performance of collective dynamics (at network level) in the face of different types of delays have taken place in the recent past: references [3], [23], [31]- [33], [35], [37], [40], [44] are few examples, although this list is not exhaustive.…”

“…Both frequency and time domain approaches are utilized in [31] to establish delay dependent and independent collective stability. Subsequently the theory was extended in [35] to the case of a network formed from a certain class of nonlinear systems. The robustness of linear consensus algorithms and conditions for convergence subject to node level self delays and relative measurement delays were developed and reported in [32] building on the research described in [31] and [35].…”

“…Subsequently the theory was extended in [35] to the case of a network formed from a certain class of nonlinear systems. The robustness of linear consensus algorithms and conditions for convergence subject to node level self delays and relative measurement delays were developed and reported in [32] building on the research described in [31] and [35]. 'Scalable' delay dependent synthesis of consensus controllers for linear multi agent networks making use of delay dependent conditions is proposed in [32].…”

Synchronization of Pulse-Coupled Oscillators and Clocks Under Minimal Connectivity Assumptions

“…In recent papers [12], [23] synchronization criteria over general strongly connected graphs have been obtained, assuming that oscillators' PRC maps are delay-advance [6] and the deviations between the initial phases are less than a half of the oscillators' period. The main idea of the proof in [12], [23] is the contracting property of the network dynamics under the assumption of delay-advance PRC, enabling one to use the maximal distance between the phases (the ensemble's "diameter") as a Lyapunov function; this approach is widely used in the analysis of Kuramoto networks [24], [25].…”