Multiple Intentional Delays Can Facilitate Fast Consensus and Noise Reduction in a Multiagent System

Tracking Control of Heterogeneous Multiagent Systems With Intrinsic Nonlinear Dynamics in Noisy and Time-Delayed Environments

This article investigates the tracking control problem of heterogeneous multiagent systems (MASs) with intrinsic nonlinear dynamics in noisy and time-delayed environments. First, a stability criterion for nonlinear stochastic delay systems with multiplicative noise and time-varying delay is proposed by applying the appropriate Lyapunov-Krasovskii functional. Then, based on the proposed stability criterion, sufficient conditions are derived for mean square (m.s.) and almost sure (a.s.) tracking of heterogeneous MASs with intrinsic nonlinear dynamics. Afterward, the above sufficient conditions further degenerate to integrator heterogeneous MASs. In particular, when the time-delay vanishes, the explicit conditions are obtained for the integrator heterogeneous MASs in the form of scalar inequalities, which can intuitively reflect the relationship between noise intensity and control gains. Finally, simulation results validate the effectiveness of the proposed control protocol.

Improving on transfer entropy-based network reconstruction using time-delays: Approach and validation

Transfer entropy constitutes a viable model-free tool to infer causal relationships between two dynamical systems from their time-series. In an information-theoretic sense, transfer entropy associates a cause-and-effect relationship with directed information transfer, such that one may improve the prediction of the future of a dynamical system from the history of another system. Recent studies have proposed the use of transfer entropy to reconstruct networks, but the inherent dyadic nature of this metric challenges the development of a robust approach that can discriminate direct from indirect interactions between nodes. In this paper, we seek to fill this methodological gap through the cogent integration of time-delays in the transfer entropy computation. By recognizing that information transfer in the network is bound by a finite speed, we relate the value of the time-delayed transfer entropy between two nodes to the number of walks between them. Upon this premise, we lay out the foundation of an alternative framework for network reconstruction, which we illustrate through closed-form results on three-node networks and numerically validate on larger networks, using examples of Boolean models and chaotic maps.

Fast consensus in a large-scale multi-agent system with directed graphs using time-delayed measurements

This article is on fast-consensus reaching in a class of multi-agent systems (MAS). We present an analytical approach to tune controllers for the agents based on the premise that delayed measurements in the controller can be preferable to standard controllers relying only on current measurements. Controller tuning in this setting is however challenging due to the presence of delays. To tackle this problem, we propose an analytic geometry approach. The key contribution is that the tuning can be implemented for complex eigenvalues of the arising graph Laplacian of the network, complementing the current state of the art, which is limited to real eigenvalues. Results, therefore, extend our knowledge beyond symmetric graphs and enable the study of the MAS under directed graphs. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.