Attack-Resilient Distributed Convex Optimization of Cyber–Physical Systems Against Malicious Cyber-Attacks Over Random Digraphs

Abstract

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 perfect 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 the global exponential convergence. Numerical simulation results are further presented to validate the effectiveness of the proposed distributed approaches.

Estimating tolerable communication delays for distributed optimization problems in control of heterogeneous multi‐agent systems

“…Remark It is indeed critical to consider communication delays when deriving stability and convergence conditions for optimization problems in multiagent systems. In the references [27] and [26], the absence of consideration for communication delays during data exchange is evident. By adopting a passive delay compensation approach, this work offers two primary advantages.…”

“…The main contributions and the closed works: Motivated by the existing literature on distributed optimization and discussions on communication networks, this paper proposes a new approach to solve the distributed optimization problem for continuous-time heterogeneous multi-agent systems with time-varying communication delays. Our approach is based on the formulation introduced in [26,27], which addresses a distributed optimization problem for continuous-time multi-agent systems. However, unlike [26,27], our approach considers communication delays and establishes a stability condition to estimate the upper bound on tolerable time delay.…”

“…Our approach is based on the formulation introduced in [26,27], which addresses a distributed optimization problem for continuous-time multi-agent systems. However, unlike [26,27], our approach considers communication delays and establishes a stability condition to estimate the upper bound on tolerable time delay. We also derive the relationship between optimal solutions and the estimation of the upper bound of time delay for the distributed optimization of heterogeneous multi-agent systems.…”

“…To solve a distributed optimization problem over Markovian switching random network communication, [25] proposed a consensus sub‐gradient algorithm with two different time‐scale step‐sizes, which is different from most existing algorithms. Additionally, the authors of [26] considered the fact that random digraphs may be caused by unreliable networks and Denial‐of‐Service attacks and investigated the problem of distributed convert optimization for linear multi‐agent systems.…”

An Adaptive Variance Reduction Zeroth-Order Algorithm for Finite-Sum Optimization

“…At present, optimization algorithms are also widely applied in practical applications, such as image recognition [1], natural language processing [2], question answering system [3], graph neural network [4], etc. In machine learning, we model the loss function of the model, then train the model through the optimization algorithm, and finally find the parameters (optimal solution) that minimize the loss of the model [5]. However, some algorithms require too many iterations in the process of finding the optimal solution, resulting in time-consuming model training.…”