Abstract
A feasible method is presented for estimating an unknown coefficient which depends on the state of a distributed system. The system is modeled by a class of nonlinear partial differential equations of parabolic type. Noisy observation data are assumed to be acquired through an arbitrary number of sensors allocated in the spatial domain. First, the asymptotic behavior of the solution to the state equation is discussed. Secondly, use is made of the maximum likelihood approach to obtain the optimal estimate of the unknown parameter. The consistency property of the optimal estimate obtained here are also shown. Finally, results of digital simulation experiments are demonstrated for the purpose of supporting the theoretical aspects.
