Distributed algorithm for resource allocation problems under persistent attacks

Abstract

This paper explores the ability of a distributed resource allocation algorithm under attacks to identify the optimal solution in the framework of hybrid dynamical systems. Since the attacks can result in time-varying topologies, differential inclusions are used to model attack modes and an average dwell-time automaton and time-ratio monitor are employed to constrain attacks. To address the effect induced by such attacks, a switched algorithm is considered. Then, to analyze stability, the switched algorithm is first modeled as a hybrid system and then a Lyapunov function is constructed to prove that the distributed algorithm under attacks is able to converge to the optimal solution of the resource allocation problem. Moreover, based on automaton and monitor constraints, an inequality condition is provided to guarantee exponential stability of the optimal solution. Finally, an example is presented to verify the theoretical result.