Abstract

This thesis deals with the problem of proper power management over asymmetric networks represented by weighted directed graphs (digraphs) in the presence of various constraints. Three different problems are investigated in this study. First, the problem of total transmission power optimization and connectivity control over the network is examined. The notion of generalized algebraic connectivity (GAC), used as a network connectivity measure, is formulated as an implicit function of the nodes' transmission powers. An optimization problem is then presented to minimize the total transmission power of the network while considering constraints on the values of the GAC and the individual transmission power levels. The problem of network lifetime maximization and connectivity control is investigated afterwards. Each node is assumed to deplete its battery linearly with respect to the transmission powers used for communication, and the network lifetime is defined as the minimum lifetime over all nodes. Finally, it is desired to maximize the connectivity level of the network with constraints on the total transmission power of the network and the individual transmission powers. The interior point and the mixed interior point-exterior point methods are utilized to transform these constrained optimization problems into sequential optimization problems. Given the new formulation, each subproblem is then solved numerically via the subgradient method with backtracking line search. A distributed version of the algorithm, taking into account the estimation of global quantities, is provided. The asymptotic convergence of the proposed centralized and distributed algorithms is demonstrated analytically, and their effectiveness is verified by simulations.