Resilient Finite Time Consensus: A Discontinuous Systems Perspective

Abstract

Many algorithms have been proposed in prior literature to guarantee resilient multi-agent consensus in the presence of adversarial attacks or faults. The majority of prior work present excellent results that focus on discrete-time or discretized continuous-time systems. Fewer authors have explored applying similar resilient techniques to continuoustime systems without discretization. These prior works typically consider asymptotic convergence and make assumptions such as continuity of adversarial signals, the existence of a dwell time between switching instances for the system dynamics, or the existence of trusted agents that do not misbehave. In this paper, we expand the study of resilient continuous-time systems by removing many of these assumptions and using discontinuous systems theory to provide conditions for normally-behaving agents with nonlinear dynamics to achieve consensus in finite time despite the presence of adversarial agents.• We demonstrate that our analysis holds for the general F -local adversarial model on digraphs, which does not assume the presence of any trusted agents. This paper is organized as follows: Section II introduces the notation and problem formulation, Section III presents our main results, Section IV gives simulations demonstrating our method, and Section V gives a brief conclusion.