Spatio-Temporal Modeling of Nonlinear Distributed Parameter Systems

From the reviews: "A distributed parameter system (DPS) is usually an engineering equivalent of a partial differential equation (PDE) or a system of PDEs. ... this book is the extension of this idea to the nonlinear setting. ... The book addresses an engineering audience, and people not very familiar with the subject will find the list of abbreviations especially useful. The chapters are inter-connected and each chapter looks like an independent entity; it starts and ends with a summary and has its own list of references ... ." (Sergey V. Lototsky, Mathematical Reviews, Issue 2012 a)

• Preface; List of Figures; List of Tables; Abbreviations; 1 Introduction; 1.1 Background; 1.1.1 Examples of distributed parameter processes; 1.1.2 Motivation; 1.2 Contributions and organization of the book; 1.3 References; 2 Modeling of Distributed Parameter Systems: Overview and Classification; 2.1 Introduction; 2.2 White-box modeling: model reduction for known DPS; 2.2.1 Eigenfunction method; 2.2.2 Green’s function method; 2.2.3 Finite difference method; 2.2.4 Weighted residual method; 2.2.4.1 Classification based on weighting functions; 2.2.4.2 Classification based on basis functions; 2.2.5 Comparison studies of spectral and KL method; 2.3 Grey-box modeling: parameter estimation for partly known DPS; 2.3.1 FDM basedestimation; 2.3.2 FEM based estimation; 2.3.3 Spectral based estimation; 2.3.4 KL based estimation; 2.4 Black-box modeling: system identification for unknown DPS; 2.4.1 Green’s function based identification; 2.4.2 FDM based identification; 2.4.3 FEM based identification; 2.4.4 Spectral based identification; 2.4.5 KL based identification; 2.4.6 Comparison studies of neural spectral and neural KL method; 2.5 Concluding remarks; 2.6 References; 3 Spatio-Temporal Modeling for Wiener Distributed Parameter Systems; 3.1 Introduction; 3.2 Wiener distributed parameter system; 3.3 Spatio-temporal Wiener modeling methodology; 3.4 Karhunen-Loève decomposition; 3.5 Wiener model identification; 3.5.1 Modelparameterization; 3.5.2 Parameter estimation; 3.6 Simulation and experiment; 3.6.1 Catalytic rod; 3.6.2 Snap curing oven; 3.7 Summary; 3.8 References; 4 Spatio-Temporal Modeling for Hammerstein Distributed Parameter Systems; 4.1 Introduction; 4.2 Hammerstein distributed parameter system; 4.3 Spatio-temporal Hammerstein modeling methodology; 4.4 Karhunen-Loève decomposition; 4.5 Hammerstein model identification; 4.5.1 Model parameterization; 4.5.2 Structure selection; 4.5.3 Parameter estimation; 4.6 Simulation and experiment; 4.6.1 Catalytic rod; 4.6.2 Snap curing oven; 4.7 Summary; 4.8 References; 5 Multi-Channel Spatio-Temporal Modeling for Hammerstein Distributed Parameter Systems; 5.1 Introduction; 5.2 Hammerstein distributedparameter system; 5.3 Basic identification approach; 5.3.1 Basis function expansion; 5.3.2 Temporal modeling problem; 5.3.3 Least-squares estimation; 5.3.4 Singular value decomposition; 5.4 Multi-channel identification approach; 5.4.1 Motivation; 5.4.2 Multi-channel identification; 5.4.3 Convergence analysis; 5.5 Simulation and experiment; 5.5.1 Packed-bed reactor; 5.5.2 Snap curing oven; 5.6 Summary; 5.7 References; 6 Spatio-Temporal Volterra Modeling for a Class of Nonlinear DPS; 6.1 Introduction; 6.2 Spatio-temporal Volterra model; 6.3 Spatio-temporal modeling approach; 6.3.1 Time/space separation; 6.3.2 Temporal modeling problem; 6.3.3 Parameter estimation; 6.4 State space realization; 6.5 Convergence analysis; 6.6 Simulation and experiment; 6.6.1 Catalytic rod; 6.6.2 Snap curing oven; 6.7 Summary; 6.8 References; 7 Nonlinear Dimension Reduction based Neural Modeling for Nonlinear Complex DPS; 7.1 Introduction; 7.2 Nonlinear PCA based spatio-temporal modeling framework; 7.2.1 Modeling methodology; 7.2.2 Principal component analysis; 7.2.3 Nonlinear PCA for projection and reconstruction; 7.2.4 Dynamic modeling; 7.3 Nonlinear PCA based spatio-temporal modeling in neural system; 7.3.1 Neural network for nonlinear PCA; 7.3.2 Neural network for dynamic modeling; 7.4 Simulation and experiment; 7.4.1 Catalytic rod; 7.4.2 Snap curing oven; 7.5 Summary; 7.6 References; 8 Conclusions; 8.1 Conclusions; 8.2 References; Index.