Z. Hidayat, R. Babuska, A. Núñez, and B. De Schutter, "Identification of distributed-parameter systems from sparse measurements," Applied Mathematical Modelling, vol. 51, pp. 605-625, Nov. 2017.
In this paper, a methodology for the identification of distributed-parameter systems is proposed, based on finite-difference discretization on a grid in space and time. It is considered the case when the partial differential equation describing the system is not known. The sensor locations are given and fixed, but not all grid points contain sensors. Per grid point, a model is constructed by means of lumped-parameter system identification, using measurements at neighboring grid points as inputs. As the resulting model might become overly complex due to the involvement of neighboring measurements along with their time lags, the Lasso method is used to select the most relevant measurements and so to simplify the model. Two examples are reported to illustrate the effectiveness of the methodology, a simulated two-dimensional heat conduction process and the construction of a greenhouse climate model from real measurements.