Observer-based Leader-following Consensus for Positive Multi-agent Systems Over Time-varying Graphs

TL;DR

This paper develops an observer-based control method for achieving leader-following consensus in heterogeneous positive multi-agent systems with time-varying communication graphs, ensuring positivity and convergence.

Contribution

It extends existing observer-based approaches to handle heterogeneous dynamics and positivity constraints in multi-agent systems over dynamic networks.

Findings

Followers maintain positive states throughout the process.

The proposed method guarantees output consensus with the leader.

Numerical simulations confirm the effectiveness of the approach.

Abstract

This paper addresses the leader-following consensus problem for discrete-time positive multi-agent systems over time-varying graphs. We assume that the followers may have mutually different positive dynamics which can also be different from the leader. Compared with most existing positive consensus works for homogeneous multi-agent systems, the formulated problem is more general and challenging due to the interplay between the positivity requirement and high-order heterogeneous dynamics. To solve the problem, we present an extended version of existing observer-based design for positive multi-agent systems. By virtue of the common quadratic Lyapunov function technique, we show the followers will maintain their state variables in the positive orthant and finally achieve an output consensus specified by the leader. A numerical example is used to verify the efficacy of our algorithms.