Delay robustness in cooperative control

Abstract

The robustness of various cooperative control schemes on large scale networked systems with respect to heterogeneous communication and coupling delays is investigated. The presented results provide delay-dependent and delay-independent conditions that guarantee consensus, rendezvous, flocking, and synchronization in different classes of multi-agent systems (MAS). All conditions are scalable to arbitrarily large multi-agent systems with non-identical agent dynamics. In particular, conditions for linear agents, for nonlinear agents with relative degree one, and for a class of nonlinear agents with relative degree two are presented. The interconnection topology between the agents is in most cases represented by an undirected graph. The results for nonlinear agents with relative degree one hold also for the more general case of directed graphs with switching topologies. Different delay configurations are investigated and compared. These configurations represent different ways how the delays affect the coupling between the agents. The presented robustness analysis considers constant, time-varying, and distributed delays in order to take different sources of delays into account. The results are applied to several typical applications and simulations illustrate the findings.

The main contributions of this thesis include: (i) Consensus and rendezvous in single integrator MAS are robust to arbitrarily large delays even on switching topologies. However, the convergence rate of this MAS is delay-dependent and scalable convergence rate conditions are presented. (ii) Consensus and rendezvous in relative degree two MAS are robust to sufficiently small delays. Local, scalable conditions are derived for these MAS that guarantee consensus and rendezvous for bounded delays. (iii) Finally, the derived delay robustness analysis for general linear MAS allows for the first time to compare different delay configurations in a unifying framework.

In dieser Dissertation wird die Robustheit von verschiedenen kooperierenden Regelungen bezüglich heterogener Kommunikations- und Kopplungsverzögerungen untersucht. Es werden skalierbare Analysemethoden für Konsens, Rendezvous, Herdenverhalten (engl. flocking) und Synchronisation für verschiedene Klassen von linearen und nichtlinearen Agentensystemen (engl. multi-agent systems) vorgestellt. Die Ergebnisse werden auf verschiedene typische Anwendungen übertragen und durch Simulationen veranschaulicht.