Continuous-Time Distributed Newton Method and Distributed Anchor-Free Network Localization

Abstract

This thesis deals with two research topics. The two topics are studies that solve optimization problems over networks. The first one is continuous-time distributed Newton method which finds the optimal solution of the strongly convex function by designing a continuous-time system over networked multi-agent systems. In the first part, we study the unconstrained strongly convex optimization based on the Newton method in the continuous time domain. The system proposed in this thesis estimates the Newton direction as a boundary-layer dynamic in the singular perturbation theory and uses the quasi-steady-state to perform a continuous-time Newton method. We explore the convergence of the algorithm and provide simulations in several settings. The second one is distributed anchor-free network localization algorithm which finds the feasible formation of sensors in wireless sensor networks under given distance constraints. In the second part, we formulate the anchor-free network localization problem into a constrained optimization and explore distributed optimization algorithms to find suitable relative positions. The distributed optimization algorithm introduced in this thesis estimates the relative positions between agents. The localization problem will be solved with respect to one common coordinate system, without using any global coordinate system. For the analysis of the proposed distributed optimization algorithm, we use the block coordinate gradient descent and asynchronous gradient-like optimization algorithm.