The problem of transport of multi-agent systems has received much attention in a wide range of engineering and biological contexts, such as spatial coverage optimization, collective migration, estimation and mapping of unknown environments. In particular, the emphasis has been on the search for scalable decentralized algorithms that are applicable to large-scale multi-agent systems.
For large multi-agent collectives, it is appropriate to describe the configuration of the collective and its evolution using macroscopic quantities, while actuation rests at the microscopic scale at the level of individual agents. Moreover, the control problem faces a multitude of information constraints imposed by the multi-agent setting, such as limitations in sensing, communication and localization.
Viewed in this way, the problem naturally extends across scales and this motivates a search for algorithms that respect information constraints at the microscopic level while guaranteeing performance at the macroscopic level.
We address the above concerns in this dissertation on three fronts: theory, algorithms and analysis. We begin with the development of a multiscale theory of gradient descent-based multi-agent transport that bridges the microscopic and macroscopic perspectives and sets out a general framework for the design and analysis of decentralized algorithms for transport. We then consider the problem of optimal transport of multi-agent systems, wherein the objective is the minimization of the net cost of transport under constraints of distributed computation. This is followed by a treatment of multi-agent transport under constraints on sensing and communication, in the absence of location information, where we study the problem of self-organization in swarms of agents. Motivated by the problem of multi-agent navigation and tracking of moving targets, we then present a study of moving-horizon estimation of nonlinear systems viewed as a transport of probability measures. Finally, we investigate the robustness of multi-agent networks to agent failure, via the problem of identifying critical nodes in large-scale networks.
