Repeated least squares with inversion and its application in identifying linear distributed-parameter systems

In the paper an approach to a certain class of nonlinear parameter estimation problem is proposed, which is, in particular, applicable to distributed parameter systems described by elliptic partial diierential equations. The approach exploits a special structure of nonlinear dependence, what allows to apply the least squares algorithm twice, together with the inversion of a nonlinear characteristic. One can rougly say that the class of considered systems can be described by a feedforeward neural net with two hidden layers and monotone activation functions. In the language of neural nets, the estimation problem can be interpreted as a partial inversion of the net, i.e., nding part of its inputs from a learning sequence. Simulations connrm that the approach is useful and much simpler than a direct iteration minimization of the sum of squares.