Identifying the parameters of infinite-dimensional systems using simple algebraic tools
Sprache des Vortragstitels:
Model-based control requires not only a mathematical model for the process to be controlled by also a sufficiently precise estimate for the physical parameters involved. While a wide range of methods is known for identifying parameters in finite-dimensional systems, usually given in terms of ordinary or algebraic equations, this is not the case for systems of infinite dimension (such as transmission or diffusion processes), where models involve partial differential equations (PDEs). As a result, most identification methods rely on finite-dimensional approximations.
In contrast, the algebraic approach presented in this talk is an exact method that does not require any approximations. It derives simple polynomial equations relating the spatially concentrated measurements and the unknown system parameters by using the Laplace transform and applying methods of commutative and differential algebra such as the Ritt algorithm and the Buchberger algorithm for computing Gröbner bases. In the end, the identification of parameters requires only the calculation of convolution products of measurement signals.
The talk will focus on the application of the algebraic identification tool to illustrative examples (of infinite-dimensional systems), including a coaxial cable modeled by the telegrapher's equations, a hydraulic transmission line given in terms of spatially two-dimensional PDEs and a cable on a crane, where the PDE describing the cable exhibits spatially dependent coefficients. Rather than discussing the general identification procedure and all mathematical proofs involved, the examples aim to give a general idea of the identification algorithm. All results, including some for fractional-order systems, are supported by either experimental or simulation data.