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Full-Text Articles in Numerical Analysis and Computation
Analytical Computation Of Proper Orthogonal Decomposition Modes And N-Width Approximations For The Heat Equation With Boundary Control, Tasha N. Fernandez
Analytical Computation Of Proper Orthogonal Decomposition Modes And N-Width Approximations For The Heat Equation With Boundary Control, Tasha N. Fernandez
Masters Theses
Model reduction is a powerful and ubiquitous tool used to reduce the complexity of a dynamical system while preserving the input-output behavior. It has been applied throughout many different disciplines, including controls, fluid and structural dynamics. Model reduction via proper orthogonal decomposition (POD) is utilized for of control of partial differential equations. In this thesis, the analytical expressions of POD modes are derived for the heat equation. The autocorrelation function of the latter is viewed as the kernel of a self adjoint compact operator, and the POD modes and corresponding eigenvalues are computed by solving homogeneous integral equations of the …
Selective Recursive Kernel Learning For Online Identification Of Nonlinear Systems With Narx Form, Yi Liu, Haiqing Wang, Jiang Yu, Ping Li
Selective Recursive Kernel Learning For Online Identification Of Nonlinear Systems With Narx Form, Yi Liu, Haiqing Wang, Jiang Yu, Ping Li
Dr. Yi Liu
Online identification of nonlinear systems is still an important while difficult task in practice. A general and simple online identification method, namely Selective Recursive Kernel Learning (SRKL), is proposed for multi-input–multi-output (MIMO) systems with the nonlinear autoregressive with exogenous input form. A two-stage RKL online identification framework is first formulated, where the information contained by a sample (i.e., the new arriving or old useless one) can be introduced into and/or deleted from the model, recursively. Then, a sparsification strategy to restrict the model complexity is developed to guarantee all the output channels of the MIMO model accurate simultaneously. Specially, a …