Networked Implementation of Continuous-Time Distributed Algorithms: A Hybrid System Approach

Abstract

With the advancements in functional capabilities of computing and communication devices, there has been a widespread interest in research and implementation of distributed (control and optimization) algorithms. These algorithms frequently find themselves in applications such as distributed computation, sensor estimation, and multi-vehicle/multi-agent coordination. In particular, the continuous-time (CT) variants of these algorithms are studied when physical entities (also referred to as agents), such as autonomous vehicles, whose dynamics naturally evolve over continuous-time, are involved. However, direct implementation of such CT variants necessitates continuous information exchange which is seldom possible. Therefore, this thesis focuses on investigating CT distributed algorithms that employ time- or event-based strategies for discrete-time communication over networks. We begin by designing event-based broadcast strategies. First, we consider a CT nonlinear system that can be stabilized with a known static state-feedback controller. We employ an emulation-based technique to implement the known controller with intermittent state updates; these updates are governed by event-triggering conditions (or ETCs which are mathematical conditions based on system variables) that dictate when the system can broadcast its state to the controller. Subsequently, we extend the study to the case of multi-agent systems (MASs) where the agents intermittently broadcast the information to their neighbors over a network. Depending on an agent's ability or inability to sense states (or relative states) of fellow agents, we design two different event-triggering mechanisms (ETMs) that help the agent in making decisions over broadcasts. We demonstrate the effectiveness of the proposed framework by offering two case studies on consensus of agents governed by nonlinear dynamics. In the aforementioned studies, the focus is on designing event-based broadcast strategies and, therefore, we have assumed that the states are broadcasted without being affected by the network itself. However, in practice, these broadcasts are often prone to several network-induced imperfections. In this thesis, we also investigate aspects of two such imperfections, namely, quantized broadcasts and transmission delays. In this regard, first, we study the problem of consensus among nonlinear agents that broadcast quantized information upon event occurrence. Second, we present a framework for distributed control of nonlinear agents where the state broadcasts take place at pre-defined sampling instants (namely, time-based broadcast strategies) and are susceptible to transmission delays. Finally, we consider a distributed optimization problem over a class of directed networks where the agents are assigned private cost functions. The agents employ CT accelerated gradient algorithm to asymptotically reach global minima; the convergence of such an algorithm is first established. Subsequently, the distributed control framework proposed earlier is adopted to enable event-based broadcasting of local decision variables. The effectiveness of the proposed methods in this thesis are demonstrated through case studies, numerical examples and, in some cases, counter-examples. Through these findings, we believe that CT distributed algorithms can be digitally implemented with some ease while simultaneously conserving energy and/or communication resources.