Distributed and robust fair resource allocation applied to virus spread minimization

This paper proposes three novel nonlinear continuous-time distributed algorithms to solve a class of fair resource allocation problems that allow an interconnected group of agents to collectively minimize a global cost function subject to equality and inequality constraints. The algorithms are robust in the sense that temporary errors in communication or computation do not change their convergence to the equilibrium, and thus, agents do not require global knowledge of total resources in the network or any specific procedure for initialization. To analyze convergence of the algorithms, we use nonlinear analysis tools that exploit partial stability theory and nonsmooth Lyapunov analysis. We illustrate the applicability of the approach via the problem of minimizing virus spread over computer and human networks.