# Resilient Leader-Follower Consensus to Arbitrary Reference Values in Time-Varying Graphs

## TL;DR

This paper introduces resilient algorithms for leader-follower consensus in time-varying networks, enabling normal agents to track arbitrary reference states despite adversarial behavior, with demonstrated simulation results.

## Contribution

It proposes novel methods for resilient leader-follower consensus in dynamic graphs, allowing tracking of external references beyond initial convex hulls, even with adversarial agents.

## Key findings

- Agents can resiliently track arbitrary reference states.
- The proposed algorithms work in time-varying graph topologies.
- Simulations confirm effectiveness under adversarial conditions.

## Abstract

Several algorithms in prior literature have been proposed which guarantee consensus of normally behaving agents in a network that may contain adversarially behaving agents. These algorithms guarantee that the consensus value lies within the convex hull of initial normal agents' states, with the exact consensus value possibly being unknown. In leader-follower consensus problems however, the objective is for normally behaving agents to track a reference state that may take on values outside of this convex hull. In this paper we present methods for agents in time-varying graphs with discrete-time dynamics to resiliently track a reference state propagated by a set of leaders despite a bounded subset of the leaders and followers behaving adversarially. Our results are demonstrated through simulations.