Autonomous and non-autonomous fixed-time leader-follower consensus for second-order multi-agent systems

TL;DR

This paper develops fixed-time consensus protocols for second-order multi-agent systems, enabling leader-follower tracking with only partial leader state access, using autonomous and non-autonomous control strategies.

Contribution

It introduces fixed-time consensus algorithms with fixed or bounded settling times, including a novel non-autonomous protocol with less conservative bounds.

Findings

Both protocols achieve fixed-time convergence.

Numerical examples demonstrate effectiveness.

Non-autonomous protocol reduces conservativeness.

Abstract

This paper addresses the problem of consensus tracking with fixed-time convergence, for leader-follower multi-agent systems with double-integrator dynamics, where only a subset of followers has access to the state of the leader. The control scheme is divided into two steps. The first one is dedicated to the estimation of the leader state by each follower in a distributed way and in a fixed-time. Then, based on the estimate of the leader state, each follower computes its control law to track the leader in a fixed-time. In this paper, two control strategies are investigated and compared to solve the two mentioned steps. The first one is an autonomous protocol which ensures a fixed-time convergence for the observer and for the controller parts where the Upper Bound of the Settling-Time (UBST) is set a priory by the user. Then, the previous strategy is redesigned using time-varying gains to obtain a non-autonomous protocol. This enables to obtain less conservative estimates of the UBST while guaranteeing that the time-varying gains remain bounded. Some numerical examples show the effectiveness of the proposed consensus protocols.