Realization of homogeneous multi-agent networks

Abstract

A class of large-scale systems with decentralized information structures, such as multi-agent systems, can be represented by a linear system with a generalized frequency variable. In these models agents are modelled through a strictly proper SISO state space model while the supervisory structure, representing the information exchange among the agents, is represented via a linear state-space model. The starting point of the paper is that the agent $h(s)$ and the overall system $\mathcal{G}(s)$ are known through their Markov parameters. Based on these data a condition is given that characterizes compatibility, i.e., the existence of a transfer function $G(s)$ that describes the network and leads to the relation $\displaystyle \mathcal{G}(s)=G \left(\frac{1}{h(s)} \right)$. If compatibility holds, the paper also presents an algorithm to compute the Markov parameters of the unknown transfer function $G(s)$. Then, a minimal state space representation of this transfer function can be computed through the Ho-Kalman algorithm.