The objective of this research award is to develop efficient, robust, and scalable distributed algorithms, which allow agents in a mobile ad hoc or sensor network to collaboratively and asynchronously solve convex and separable constrained optimization problems over the network. The approach is based on a blend of tools and ideas from control theory, optimization theory, and wireless networking, bringing together notions of feedback iteration control, Lyapunov stability concepts, networked dynamical systems, Lagrange multiplier methods, and protocol design techniques. The problems to be addressed include general convex program and its two important special cases, linear and quadratic programs. The models to be studied include models with static and dynamic problem data, agent memberships, and network topologies. The deliverables include a collection of distributed algorithms, theoretical analysis of their behaviors, computer simulation of their performances, documentation of the research outcomes, and integration of the research with high school, undergraduate, and graduate education.
If successful, the results of this research will enhance the capability and functionality of mobile ad hoc and wireless sensor networks, enabling agents to cooperatively accomplish sophisticated tasks that require fusion of information, decentralized decision making, and coordination of actions. These will, in turn, broaden the scientific and engineering applications of such networks. The results will also make contributions to control theory by creating a new paradigm in control of multi-agent systems, namely, Lyapunov-based feedback control of when to communicate and compute, so that agents can achieve optimized global behavior quickly through minimal local interactions. Integration of the research with education will benefit high school students via outreach activities and robotics competition mentorship, undergraduate students via classroom instruction and an NSF Research Experiences for Undergraduates grant, and graduate students via research supervision and offering of a new graduate course.