Minimal-time network reconstruction for DTLTI systems

This paper considers the problem of obtaining in minimal time the “dynamical network structure” (DNS) from partial state observations of a discrete-time linear time-invariant system. From the DNS, we can not only obtain the network structure of the system at the measurement level, but also estimate the minimal number of hidden states which are not observed directly. First, we discuss when reconstruction of the DNS is and is not possible. Then, we give an algorithm to find the minimal number of successive outputs to find the DNS. Finally, we discuss extensions of the results to non-linear and noisy systems. These results can be directly applied to the decentralised network control problem of multi-agent systems to find network connections of the observed agents.