An algebraic algorithm for parameter identification in a class of systems described by linear partial differential equations

The identification of parameters in systems described by one-dimensional linear partial differential equations with constant coefficients is addressed. The algebraic approach used for identification has previously been applied to different infinite dimensional systems. Here, an algebraic algorithm is presented generalizing the underlying ideas from these examples to the class of systems mentioned before. It derives simple polynomial equations relating the concentrated measurements and the unknown parameters by using the Laplace transform and applying methods of commutative and differential algebra such as the Ritt algorithm. In the end, the identification of parameters requires only the calculation of convolution products of measurement signals. A vibrating string serves to illustrate the theory. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)