A subspace identification of deterministic part of state space model operating in closed-loop

This paper solves the problem of identifying the deterministic part of the plant operating in closed-loop. Under the assumption that the exogenous reference input is feedback-free and persistently exciting (PE), it can be shown that the identification of the deterministic part is independent of the identification of the stochastic part by the preliminary orthogonal decomposition of the joint input-output data of the plant. Thus the deterministic part is identified by applying any deterministic subspace identification method to the deterministic component of the joint process, followed by a (balanced) model reduction. Some numerical results are included to show the applicability of the present technique.