| The thesis develops methodology and algorithms to study distributed inference problems in large scale networked systems. Typical examples that fall under the scope of this study include distributed detection, distributed field reconstruction (estimation) arising in wireless sensor network (WSN) applications, and filtering in networked dynamical (cyberphysical) systems. The systems in question operate in random environments and are constrained in terms of resources, like communication bandwidth or power. Due to the inherent randomness in sensor deployment or field sampling, often there is no center coordinating the network activity. The nodes (sensors or dynamical agents) need to collaborate with each other through local information exchange to achieve desired global network behavior. One aspect of our work involves the development of robust distributed algorithms for collaborative information processing in these networks. We study the performance of these distributed schemes in terms of their robustness to communication failures, external stochastic perturbations, and convergence to the corresponding centralized counterparts. The other aspect of the work addresses fundamental system theoretic questions in such networked settings. For example, we formulate notions of observability in distributed estimation and stability and robustness of distributed filters in the face of non-classical and uncertain information patterns. The technical tools used in the study include mixed time scale stochastic approximation, random dynamical systems, and large deviation theory. Our methods are generic and often contribute to the general theory of these classical disciplines. |
