Identification of distributed parameter systems via multidimensional distributions

The paper presents a method of determining the parameters of a process described by a partial differential equation from a knowledge of its solution. The development is based on treating the process signals as multidimensional distributions in the manner established by Laurent Schwartz, and expanding them in an exponentially weighted series of the generalised partial derivatives of the multidimensional Dirac delta function, termed as the Poisson moment functional ( p. m. f. ) expansion. The ability of the method is successfully demonstrated in the presence of noise.