Positive consensus of multi-agent systems with hierarchical control protocol

In this paper, the positive state consensus problem of a network of homogeneous LTI positive agents is presented. A hierarchical control protocol is applied to achieve finite positive state consensus over directed networks. The minimal state-space realization considered for the interconnected positive agents is not restricted to be (internally) positive state-space realization, which is in contrast to the existing literature. A set of sufficient conditions is derived in linear programming framework which is solved to find controller gain matrices involved in the consensus protocol. Also, in this paper, an observer-based hierarchical control protocol has been derived to achieve finite positive state consensus. Numerical examples are given to demonstrate the usefulness of the proposed results. (c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper introduces the positive state consensus problem of a network of homogeneous LTI positive agents, and applies a hierarchical control protocol to achieve finite positive state consensus over directed networks. The minimal state-space realization for the interconnected positive agents is derived without the restriction of an internally positive state-space realization. A set of sufficient conditions and controller gain matrices are obtained through linear programming framework, and an observer-based hierarchical control protocol is proposed for achieving finite positive state consensus. Numerical examples are provided to demonstrate the usefulness of the proposed results.