STOCHASTIC OPTIMIZATION AND ITS APPLICATION TO COMMUNICATION NETWORKS AND THE SMART GRID By ZONGRUI DING A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy STOCHASTIC OPTIMIZATION AND ITS APPLICATION TO COMMUNICATION NETWORKS AND THE SMART GRID By Zongrui Ding August 2012 Chair: Dapeng Wu Major: Electrical and Computer Engineering The scheduling of some practical systems is highly affected by the randomness of the system variables. Therefore, it is of great importance to model and optimize the system performance by stochastic optimization techniques. This work presents the results of stochastic optimization with application to the scheduling in two important areas: the multi-hop wireless networks and the Smart Grid. The wireless multi-hop networks are typically modeled as systems consisted of multiple queues. Our work is built under the Per-link (PL) queueing structure, which is more scalable compared with the per-destination (PD) queueing structure. We mainly focus on the scheduling of the PL queueing networks involving link scheduling, power allocation and routing under the network stability. For the Smart Grid systems, we study the integration of renewable resources for Distributed Energy Resources (DERs) in the hybrid power system. In Chapter 2 and 3, we consider the joint problem of congestion control and scheduling with multi-class Quality of Service (QoS) requirements in wireless multi-hop networks under both time invariant and time-varying channels. Generally, the joint problem is formulated as a Network Utility Maximization (NUM) problem and can be solved by the back-pressure algorithm under PD queueing. The PD queueing requires that each node maintains a separate queue for each destination. We consider the PL queueing, which reduces the queue number per node to the number of node neighbors. Based on this queueing model, we propose a Sliding Mode (SM) approach to designing