Modeling and identification of periodically time-varying dynamical systems

April 25, 2014

I study modeling and identification of periodically time-varying dynamical systems. Such systems exhibit a significantly more complicated dynamic behavior than non-periodic systems. Identification of sufficiently accurate models and controlling of such systems is therefore a non-trivial problem. The target of my study is to develop practically useful methods for identification and controlling of periodic systems.

One aim is to obtain accurate state-space models for periodic dynamical systems by using orthonormal filters, such as Laguerre or Kautz filters (1,2). Good results have been obtained for linear time-invariant systems but heretofore identification of periodic dynamical systems has not been studied comprehensively. The accuracy of the identified model depends considerably on the poles of the applied filters. Thus one of the main problems of my research is to select the filter poles properly.

Another goal is to develop precise and efficient subspace identification method for periodic dynamical systems. Subspace identification methods (3) are based on the geometric projections and these methods exploit the row or the column subspace of a certain matrix to obtain the state-space matrices of an identified system.

Some references

(1) B.Wahlberg. System identification using Laguerre models. IEEE Transactions on Automatic Control, 36, 551-562, 1991.

(2) B. Wahlberg. System identification using Kautz models. IEEE Transactions on Automatic Control, 39, 1276-1282, 1994.

(3) P. Van Overschee and B. De Moor. Subspace identification for linear systems: theory – implementation – applications. Springer, 1996.