Approximation of Large-Scale Dynamical Systems

By Athanasios C. Antoulas. Advances in Design and Control, 2005

3,362 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/31a9c66730500929663f23fc8350a190b471422e

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Citations in the corpus

A Riemannian Optimization Approach for Computing Low-Rank Solutions of Lyapunov Equations (2010, background): “Lyapunov equations are of significant importance in control theory [8], model reduction [33], and stochastic analysis of dynamical systems [41]; see [4] for a general overview.”
Model Reduction by Moment Matching for Linear and Nonlinear Systems (2010, methodology): “Remark 5: The proposed approach differs from the interpolation/projection approach developed, for example, in [1].”
Computational Methods for Linear Matrix Equations (2016, background): “, [4],[109],[115] and references therein.”
Efficient Computation of Multivariable Transfer Function Dominant Poles Using Subspace Acceleration (2006, methodology): “A survey on model reduction methods employing either singular value decompositions or moment matching based methods is found in [8,9].”
Handbook of Big Data (2016, neutral): “More details about the SVD algorithm can be found in [4] and [2].”
Generalized multiscale finite element methods (GMsFEM) (2013, background): “, [39, 18, 6, 54]) construct a space of global fields that can approximate the solution space.”
Stability analysis of positive descriptor systems (2008, background): “Positive standard systems, i.e., where E is the identity matrix, are subject to ongoing research by many authors [1,17,18,22,26,36,37,38,40,41].”
A Survey on Model Reduction of Coupled Systems (2008, methodology): “In the last years, many different model reduction methods have been developed in computational fluid dynamics, control design and electrical and mechanical engineering, see [3, 11, 47] for books on this topic.”
Approximation errors in nonstationary inverse problems (2007, methodology): “The reduced model (2) is usually obtained by using systematic model reduction techniques that focus on the approximation of the the mappings fk and gk, see for example [2].”
FACTORIZED SOLUTION OF SYLVESTER EQUATIONS WITH APPLICATIONS IN CONTROL (2004, background): “If (A,C) is observable and (H,F ) is controllable, then a unique full-rank solution of theSylvester observer equation HX − XA + FC = 0 exists and with G := XB, the solution z(t) of (11) is a state observer for any initial values x0, z(0), and any input function u(t).”
Control and Optimization with Differential-Algebraic Constraints (2012, background): “This is mainly due to the fact that the constraints and physical properties, like stability and passivity, must be respected in the approximated model to achieve physically meaningful results [1, 35].”
Provably Convergent Multifidelity Optimization Algorithm Not Requiring High-Fidelity Derivatives (2012, background): “order modeling [4], or using coarser discretizations [5], can generate surrogates of high-fidelity analyses that may be treated as lowerfidelity models.”
Elastic PMLs for resonator anchor loss simulation (2005, background): “Krylov-subspace projections are often used to build reduced models of large systems [6, 3].”
Efficient computation of transfer function dominant poles using subspace acceleration (2006, methodology): “A good survey on model reduction methods employing either singular value decompositions or moment matching-based methods is found in [9], [10].”
Parametric Order Reduction of Proportionally Damped Second Order Systems (2006, background): “1 Introduction Model order reduction based on Krylov subspaces [2, 7] has been originally developed for the reduction of first order systems.”
A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control (2013, methodology): “[2].”
An Error Analysis of Galerkin Projection Methods for Linear Systems with Tensor Product Structure (2013, positive): “Sylvester equations arise in the context of numerical methods for eigenvalue problems [9, 13], algebraic Riccati equations [5], and model reduction [1].”