Abstract

When designing a wireless network, an important factor to control is the power that is transmitted by each individual node. We require this power to be high enough that the connection remains reliable, but not so high that it might cause significant interference in the signal of neighboring nodes. Control of the power allocations is thus a topic that has been extensively studied in recent years. Now, however, we see a proliferation in the use of mobile wireless devices. These mobile devices give rise to a relative motion of the nodes of the network, giving the system model an explicit time-dependence. In this talk we will consider a general class of distributed algorithms for the control of power allocations in such time-varying wireless networks. We will utilise appropriately constructed Lyapunov and Lyapunov-Razumikhin functions to prove the global asymptotic stability of these algorithms, even in the more complicated, physically relevant situation where the system incorporates heterogeneous, time-varying delays. These conclusions will then be illustrated by consideration of a simplified numerical example of a wireless system with its users in relative motion.

The work presented in this talk is joint work with Dr. Ioannis Lestas of the Department of Engineering, University of Cambridge.