  This paper addresses a resilient exponential distributed convex optimization
problem for a heterogeneous linear multi-agent system under Denial-of-Service
(DoS) attacks over random digraphs. The random digraphs are caused by
unreliable networks and the DoS attacks, allowed to occur aperiodically, refer
to an interruption of the communication channels carried out by the intelligent
adversaries. In contrast to many existing distributed convex optimization works
over a prefect communication network, the global optimal solution might not be
sought under the adverse influences that result in performance degradations or
even failures of optimization algorithms. The aforementioned setting poses
certain technical challenges to optimization algorithm design and exponential
convergence analysis. In this work, several resilient algorithms are presented
such that a team of agents minimizes a sum of local non-quadratic cost
functions in a safe and reliable manner with global exponential convergence.
Inspired by the preliminary works in [15]-[18], an explicit analysis of
frequency and duration of attacks is investigated to guarantee exponential
optimal solutions. Numerical simulation results are presented to demonstrate
the effectiveness of the proposed design.
