Finite-Time Resilient Formation Control with Bounded Inputs

TL;DR

This paper presents a novel finite-time resilient formation control method for multi-agent systems with bounded inputs, employing a norm-based filtering mechanism and a resilient directed acyclic graph structure to ensure convergence despite adversarial agents.

Contribution

Introduces a continuous-time resilient controller with input bounds and a graph-theoretic condition (RDAG) for finite-time convergence in multi-agent formation control.

Findings

Guarantees convergence in finite time under RDAG conditions

Employs a norm-based filtering mechanism for robustness

Demonstrates exponential convergence in discrete-time systems

Abstract

In this paper we consider the problem of a multi-agent system achieving a formation in the presence of misbehaving or adversarial agents. We introduce a novel continuous time resilient controller to guarantee that normally behaving agents can converge to a formation with respect to a set of leaders. The controller employs a norm-based filtering mechanism, and unlike most prior algorithms, also incorporates input bounds. In addition, the controller is shown to guarantee convergence in finite time. A sufficient condition for the controller to guarantee convergence is shown to be a graph theoretical structure which we denote as Resilient Directed Acyclic Graph (RDAG). Further, we employ our filtering mechanism on a discrete time system which is shown to have exponential convergence. Our results are demonstrated through simulations.