Some algorithmic aspects of subspace identification with inputs (Q2716502)

Identification of linear dynamic systems described by state space models is considered. It is assumed that only the input and the disturbed output can be measured. Therefore a ``true stochastic'' system must be investigated. Since the state of the system is not available, the system matrices must be identified in a subspace.NEWLINENEWLINENEWLINETwo approaches are considered: The orthogonal decomposition approach with disjoint deterministic and stochastic parts and the joint approach with common dynamics for the two components. An algorithm for solving the identification problem is presented. NEWLINENEWLINENEWLINEThe algorithm consists of four steps. In the first step the state space and an extended observability matrix are estimated. In the second step the system matrix and the output matrix are determined. The Kalman gain for the stochastic part of the system is computed in the third step. Finally the input matrices are estimated.NEWLINENEWLINENEWLINEA brief overview of the main procedures is given. Simulation results are presented. A MATLAB software package is available from the first author.