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Robust Coordination and Control of Networked Systems with Intermittent Communication

Abstract

Networked systems characterize many modern real-world interactions, ranging from the internet and social media networks, to communication networks and power distribution networks, to interconnected neuron and biological models. For such networks, agents in the network utilize information from its neighbors to achieve a common task, however, in practical applications the information available to each agent may not be continuously available. Moreover, such information may be subjected to environmental perturbations. Therefore, in this dissertation, robust coordination and control algorithms are studied for networked systems when the coupling between them are naturally intermittent. Namely, coordination in terms of synchronization and desynchronization for different interconnected networked systems are analyzed. The intermittency of the communication structure implies some impulsive instances in the dynamics, therefore, for each case, a hybrid systems approach is utilized to model and analyze the dynamics of such systems. Namely, results for set stability using Lyapunov stability and invariance principles are utilized to study the dynamical properties of the coordination algorithms. This dissertation is divided into two enveloping parts: 1) controller design for the synchronization of continuous-time agents where the information transmitted between the agents is intermittent; 2) a dynamical study of desynchronization in impulse-coupled oscillators with some resulting applications. More specifically, the first part considers a distributed controller design for the case when each agent has linear time-invariant continuous-time dynamics, however, the communication triggering information transfer between agents occurs intermittently. For this case, the robust exponential stability of the set characterizing synchronization in continuous linear time-invariant systems when information from neighbors is received impulsively at isolated time instances. The second part considers the case of a network of impulse-coupled oscillators. Impulse coupled oscillators are systems which evolve continuously, until a threshold is reached, at which point, releases an impulse and affects neighboring agents. Due to the oscillatory nature of such systems, under certain parameters the times at which impulses occur separate in time, this action is referred to as desynchronization. The set of points describing desynchronization is characterized and recast as a set stabilization problem, it is shown that the desynchronization set is robustly asymptotically stable. Utilizing recent results for impulse coupled oscillators, applications to the study of dynamical behavior of spiking neurons and to frequency rendezvous for communication systems are given.

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