Stability analysis of distributed convex optimization under persistent attacks: A hybrid systems approach

In this paper, a distributed convex optimization algorithm under persistent attacks is investigated in the framework of hybrid dynamical systems. The existence of attacks may influence the behavior of an algorithm that solves the optimization problem. In this case, an interesting question is under what conditions the optimal solution can be found. To explore this problem, we first use differential inclusions to model attack modes and then use an average dwell-time automaton and time-ratio monitor to constrain attacks. Then based on these constraints, an inequality condition is given to ensure exponential stability of the optimal solution. Finally, a switched algorithm is modeled as a hybrid dynamical system and a Lyapunov function is constructed to show the optimal solution can be achieved exponentially under persistent attacks. (C) 2019 Elsevier Ltd. All rights reserved.