State-space models from time-series as solutions of least-squares equations

Abstract

State-space models with block-diagonal system matrices allow for straightforward control system design. Often, however, methods to block-diagona lize suffer from numerical instabilities. The author investigates a technique that would obtain such models as the solution to a set of linear equations. The work follows and extends a method due to Moonen informally known as the two-stage method1. Using this procedure, a state vector sequence is obtained which is consistent with input-output data, and then the system matrices are obtained by solving a set of linear equations in the least squares sense. An algorithm for constraining the solution to a block-diagonal set has been completed and tested. However, initial investigation showed that the necessary state vector sequence does not come directly from Moonen's procedure. The current work is to find a transformation on the state-vector sequence that will yield the desired form of the model. Once this step is achieved, an automated process of testing the validity of the model will also be implemented, resulting in a useful and innovative tool for system identification and control system design.