Abstract
The problem of identifying system parameters for time-invariant distributed parameter systems subject to unknown boundary conditions and initial conditions is investigated. An extension of the linear integral filter is made for handling partial derivatives of multi-variable functions. In the noise-free case, applying the extended linear integral filter to the nonlinear partial differential equation leads to an integral equation, and then the unknown system parameters are obtained conveniently using an on-line least squares algorithm. In the noisy case, instrumental variables are introduced in the gradient of the criterion function, and the method of stochastic approximations (SA) is employed to obtain consistent estimates. This method does not require as much information on the noise statistics as the bias-compensating SA methods. A number of illustrative numerical examples are also included.
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