Spatio-temporal modeling of nonlinear distributed parameter systems. A time/space separation based approach.
The book surveys a number of modeling techniques. Spatiotemporal models with space-time separation are the main focus of the book. A typical model in the book is mathematically described by a quasi-linear diffusion-advection equation. Such models have numerous industrial applications: chemical reactors, ovens, etc. In many situations, not all crucial parameters of the system are available for direct measurement. A distributed system is usually controlled by a finite number of actuators. The models are classified as white box, grey box, and black box, depending on the availability of information. System identification and model reduction are the main subjects of the book. After a general introduction in Chapter~1, Chapter~2 overviews a classification of distributed-parameter systems and methods of identification. Chapter~3 considers Wiener modeling approach. Hammerstein approach is considered in Chapter~4 and generalized to multi-channel modeling in Chapter~5. Volterra approach with Green-function kernel is the subject of Chapter~6. Chapter~7 presents nonlinear principal-component analysis. Chapter~8 summarizes the contents of the book and formulates the conclusions. In the authors' words, ``there are some challenges which have not been well studied in system identification of the distributed-parameter systems''.
scientific article; zbMATH DE number 5852764