Attack-Resilient Distributed Convex Optimization of Linear Multi-Agent Systems Against Malicious Cyber-Attacks over Random Digraphs

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.