Problems in Distributed Sensing and Control

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Current interest in distributed control has led to a very rapid increase in the application of graph theoretic ideas to problems of analyzing and synthesizing a variety of desired behaviors such as swarming, rendezvousing, reaching a consensus, as well as well as a variety of sensing and communication tasks associated with distributed averaging, search and rescue, environmental monitoring, security, etc. While this in-depth assault on these problems using a combination of graph theory and system theory has been underway for some time, it is likely to significantly expand in the years to come. One example of this is the resurgence of interest in structural controllability and its applications to swarming, complex social networks and network security. Another is the explosion of interest in the development of distributed computational procedures for addressing basic numerical problems such as estimating parameters of a linear system, solving a distributed optimization problem or solving a system of possibly nonlinear algebraic equations. Still another is the extremely active area of network security. In broad terms these are the three problem areas upon which this project will focus.The research to be undertaken will address distributed sensing and control on three clearly defined fronts. (1) A study will be made of the genericity with respect to specific perturbation classes of various fundamental properties of linear dynamic systems such as controllability and spectrum assignability. Many classical results already exist for linear models in which algebraically independent parameters enter a model's system matrices "linearly" at unique locations. The novelty of the research to be undertaken in this project is that it is aims to deal with the commonly encountered situation in which the same parameter appears in a model's systems matrices in multiple location. An attempt will be made to characterize in graph theoretic terms significantly more general notions of structural controllability and structurally fixed modes than are currently available. (2) An effort will be made to develop distributed and asynchronous algorithms for solving certain systems of nonlinear algebraic equations which arise in connection with distributed optimization and estimation problems across a given network of autonomous agents assuming limited communication between agents and time-varying networks. Questions of convergence rate, robustness and stability of these algorithms will be addressed, as will the effects of intermittent data transmissions and transmission delays. (3) An exploration will be made of various algorithms based on game theory for searching across a physical network with the goal of capturing or otherwise defeating an intruder intent on causing a disruption. The games will be formulated between two players, namely the intruder and a surveillance agent whose job is to thwart the intruder. Various types of static and dynamic games will be considered.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.