Repeated least squares with inversion and its application in identifying linear distributed-parameter systems
Ewaryst Rafajłowicz · International Journal of Systems Science · 2000
In the paper an approach to a certain class of the nonlinear parameter estimation problem is proposed, which is, in particular, applicable to distributed-parameter systems described by elliptic partial differential equations. The approach exploits the special structure of nonlinear dependence, which allows the least-squares algorithm to be applied twice, together with the inversion of a nonlinear characteristic. One can roughly say that the class of considered systems can be described by a feedforward neural net with two hidden layers and monotonic activation functions. In the language of neural nets, the estimation problem can be interpreted as a partial inversion of the net, that is finding part of its inputs from a learning sequence. Simulations confirm that the approach is useful and much simpler than a direct iteration minimization of the sum of squares.