Robust Positive Consensus for Heterogeneous Multi-agent Systems

TL;DR

This paper develops a robust positive consensus method for heterogeneous multi-agent systems with state variables confined to the positive orthant, ensuring stability and pattern fulfillment despite external inputs and switching topologies.

Contribution

It introduces a novel two-step design involving positive local reference generators and decentralized controllers for robust consensus in heterogeneous systems.

Findings

Ensures finite-gain stability under switching topology.

Validates effectiveness through simulation example.

Achieves robust consensus with prescribed patterns.

Abstract

This paper investigates a robust positive consensus problem for a class of heterogeneous high-order multi-agent systems subject to external inputs. Compared with existing multi-agent consensus results, the most distinct feature of the formulated problem is that the state variables of all heterogeneous agents are confined in the positive orthant. To solve this problem, we present a two-step design procedure. By constructing an auxiliary multi-agent system as positive local reference generators, we incorporate the reference generator into some applicable decentralized robust tracking controller for each agent. The proposed distributed algorithm is proven to ensure a robust consensus fulfilling certain prescribed pattern for the multi-agent system under switching topology in the sense of finite-gain stability with respect to the external inputs. A simulation example is finally given to illustrate the effectiveness of our design.