Continuous-time System Identification of Nonparametric Models with Constraints. Wang, L., Gawthrop, P., & Young, P. In
abstract   bibtex   
Although structural constraints such as model order and time delay have been incorporated in the continuous time system identification since its origin, the constraints on the estimated model parameters were rarely enforced. This paper proposes a continuous time system identification approach with constraints. It shows that by incorporating physical parameter information known a priori as hard constraints, the traditional parameter estimation schemes are modified to minimize a quadratic cost function with linear inequality constraints. Using the structure of Frequency Sampling Filters as the vehicle, the paper shows that the constraints can be readily imposed on continuous time frequency response estimation and step response estimation. In particular, a priori knowledge in both time-domain and frequency domain is utilized simultaneously as the constraints for the optimal parameter solution. A Monte-Carlo simulation study with 100 noise realization is used to demonstrate the improvement of the estimation results in terms of continuous time frequency response and continuous time step response.
@inproceedings{WanGawYou05,
  author = {L. Wang and P.J. Gawthrop and P.C. Young},
  title = {Continuous-time System Identification of Nonparametric Models
                  with Constraints},
  crossref = {IFAC16},
  abstract = {Although structural constraints such as model order
                and time delay have been incorporated in the
                continuous time system identification since its
                origin, the constraints on the estimated model
                parameters were rarely enforced. This paper proposes a
                continuous time system identification approach with
                constraints.  It shows that by incorporating physical
                parameter information known a priori as hard
                constraints, the traditional parameter estimation
                schemes are modified to minimize a quadratic cost
                function with linear inequality constraints. Using the
                structure of Frequency Sampling Filters as the
                vehicle, the paper shows that the constraints can be
                readily imposed on continuous time frequency response
                estimation and step response estimation. In
                particular, a priori knowledge in both time-domain and
                frequency domain is utilized simultaneously as the
                constraints for the optimal parameter solution. A
                Monte-Carlo simulation study with 100 noise
                realization is used to demonstrate the improvement of
                the estimation results in terms of continuous time
                frequency response and continuous time step response.}
}

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