Gramian-Based Model Reduction for Data-Sparse Systems
نویسندگان
چکیده
منابع مشابه
Gramian-Based Model Reduction for Data-Sparse Systems
Model reduction is a common theme within the simulation, control and optimization of complex dynamical systems. For instance, in control problems for partial differential equations, the associated large-scale systems have to be solved very often. To attack these problems in reasonable time it is absolutely necessary to reduce the dimension of the underlying system. We focus on model reduction b...
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Model order reduction (MOR) is common in simulation, control and optimization of complex dynamical systems arising in modeling of physical processes and in the spatial discretization of parabolic partial differential equations (PDEs) in two or more dimensions. Typically, after a semidiscretization of the differential operator by the finite element method (FEM) or by the boundary element method,...
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Model reduction is of fundamental importance in many control applications. We consider model reduction methods for linear time-invariant continuous-time descriptor systems. These methods are based on the balanced truncation technique and closely related to the controllability and observability Gramians and Hankel singular values of descriptor systems. The Gramians can be computed by solving gen...
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We consider linear time-invariant (LTI) systems of the following form Σ : { ẋ(t) = Ax(t) + Bu(t), t > 0, x(0) = x, y(t) = Cx(t) + Du(t), t ≥ 0, with stable state matrix A ∈ Rn×n and B ∈ Rn×m, C ∈ Rp×n, D ∈ Rp×m, arising, e.g., from the discretization and linearization of parabolic PDEs. Typically, in practical applications, we have a large state-space dimension n = O(105) and a small input and ...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2008
ISSN: 1064-8275,1095-7197
DOI: 10.1137/070711578