Numerical integration approach to on-line identification of continuous-time systems

Abstract

Abstract The problem of estimating the parameters in linear continuous differential equation models from sampled data is treated. Using a linear integral filter, we can obtain an identification model that is parametrized directly in the continuous-time model parameters. The unknown initial states of the system do not require estimation. The choice of the sampling interval and the design of the linear integral filter are discussed considering the accuracy of parameter estimates and the computational burden. By applying the results from discrete-time model identification with the obtained identification model, a discrete-time parameter estimation method is developed, and the necessary condition as well as the sufficient condition on the input for consistency are explicitly derived and discussed in particular situations. A simulation study is also included to confirm the theoretical results.