A Mathematical Framework for Interconnected Systems Operating in a 1-D Network
Jean E. Piou · 2019
A technique to compute the global state space matrices of an interconnected one dimensional (1-D) network from input-output data or simply from output data of local systems with non-accessible inputs is investigated. First, a Hankel matrix carried out on the data allows, via low-rank truncation, the computation of full state matrices from which the global state transition and observation matrices of the network are obtained and its control matrix is obtained via a least-squares of an observability Gramian onto the data. Next, the state matrices of the local systems are extracted from the global state matrices of the network. The proposed technique is tested on radar data collected on a canonical target over 1 GHz bandwidth and 12.75 degree aspect angles where data from each frequency over the range of viewing angles is considered as output from a local system. The technique provides full state matrices that mimic well the true data, global state matrices that provide the trends depicted in truth and the state interconnections that give the dynamics of the local systems.