Article
Automation & Control Systems
Lyes Nechak, Henri-Francois Raynaud, Caroline Kulcsar
Summary: This article presents a method to address high-order stochastic linear quadratic (LQ) control problems using random parameter-dependent truncated balanced realization (RPD-TBR), which is more effective in handling LQ gain selection and performance evaluation for plants with probabilistic uncertainty compared to the original RPD full state model.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2021)
Article
Mathematics, Applied
Christian Schroeder, Matthias Voigt
Summary: In standard balanced truncation model order reduction, the initial condition is typically ignored, but the proposed balancing procedure based on state shift transformation can yield a better reduced-order model with a priori error bound. Additionally, the paper discusses the construction of reduced-order models and the efficient optimization of error bounds.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics
Caixing Gu, Shuaibing Luo
Summary: The paper examines the invariant subspaces of shift operators on vector-valued Hardy spaces and their relation to bilateral shift operators. By establishing a one-to-one correspondence, the invariant subspaces of S-E circle plus S-F* are linked to a class of invariant subspaces of bilateral shifts. The results are expressed as kernels or ranges of specific operators, expanding and providing different proofs for previous research findings.
JOURNAL OF FUNCTIONAL ANALYSIS
(2022)
Article
Automation & Control Systems
Muhammad Imran, Muhammad Imran
Summary: In this article, a two-dimensional model reduction method based on minimal rank-decomposition condition and time-limited Gramians is proposed, which works for both one-dimensional and two-dimensional systems. Compared to existing methods, this approach provides an easily computable a priori error-bound formulation and demonstrates good simulation results.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Automation & Control Systems
Muhammad Imran, Muhammad Imran
Summary: Dealing with two-dimensional models is challenging due to their complex structure. Existing model reduction methods suffer from stability issues and approximation errors. In this research, a new time-weighted stability-preserving model reduction method is proposed, along with a priori error bounds for both one-dimensional and two-dimensional models.
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE
(2022)
Article
Engineering, Electrical & Electronic
Zeinab Salehi, Paknoosh Karimaghaee, Mohammad-Hassan Khooban
Summary: This paper introduces a novel model reduction scheme that aims to preserve both positive realness and bounded realness properties of a system simultaneously. The method utilizes positive real and bounded real Riccati equations, and balances the gramians extracted from these equations based on the Balanced Truncation concept. A numerical example is provided to demonstrate the effectiveness of the proposed method.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2021)
Article
Mathematics, Applied
Peter Benner, Steffen W. R. Werner
Summary: This paper discusses the extension of frequency- and time-limited balanced truncation methods to second-order dynamical systems for practical applications. Numerical methods and modifications for large-scale sparse matrix equations are presented, along with three numerical examples for illustration.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2021)
Article
Mathematics, Applied
Ines Dorschky, Timo Reis, Matthias Voigt
Summary: We introduce a model reduction approach for linear time-invariant second order systems based on positive real balanced truncation. Our method guarantees to preserve asymptotic stability and passivity of the reduced order model as well as the positive definiteness of the mass and stiffness matrices. Moreover, we receive an a priori gap metric error bound. Finally we show that our method based on positive real balanced truncation preserves the structure of overdamped second order systems.
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
(2021)
Article
Engineering, Electrical & Electronic
Zeinab Salehi, Paknoosh Karimaghaee, Mohammad-Hassan Khooban
Summary: This paper discusses model order reduction for positive real systems using the mixed gramian balanced truncation (MGBT) method, which aims to reduce computational effort and provide error bounds. Novel modifications to MGBT have been developed to address its disadvantage of not providing error bounds, showing better performance compared to traditional methods like positive real balanced truncation (PRBT). Comprehensive numerical examples are included to demonstrate the effectiveness of the proposed methods.
CIRCUITS SYSTEMS AND SIGNAL PROCESSING
(2021)
Article
Mathematics, Applied
Josie Koenig, Melina A. Freitag
Summary: This paper discusses the application of balanced truncation to linear Gaussian Bayesian inference, particularly the 4D-Var method, and strengthens the connection between systems theory and data assimilation. The similarities between both types of data assimilation problems allow for the generalization of the state-of-the-art approach, proposing an enhanced method to balance Bayesian inference for unstable systems and improve numerical results for short observation periods.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Automation & Control Systems
Guoyun Zhang, Yao-Lin Jiang, Kangli Xu
Summary: In this paper, a new model reduction method for quadratic-bilinear systems based on time-interval Gramians is presented. The solvability conditions for generalized Lyapunov equations, whose solutions are exactly time-interval Gramians, are derived. Lyapunov stability and error bound are discussed to demonstrate the improvement of time-interval balanced truncation. The numerical results illustrate the enhanced accuracy and robustness.
ASIAN JOURNAL OF CONTROL
(2023)
Article
Mathematics, Interdisciplinary Applications
S. Galatolo, M. Monge, I. Nisoli, F. Poloni
Summary: In this paper, we propose a comprehensive framework for the rigorous approximation of invariant densities and other statistical features of dynamics. Our method utilizes a finite element reduction and a suitable finite dimensional projection to approximate the system. We introduce a novel coarse-fine strategy that leverages a coarser approximation of the system to speed up computation and estimate invariant densities and the speed of mixing.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
G. Ramesh, Shanola S. Sequeira
Summary: This article characterizes Toeplitz AN-operators and discusses some results on the minimum modulus of Toeplitz operator T-phi. It also obtains an improved result regarding the essential infimum of the modulus of a certain function.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Engineering, Mechanical
Alexandre Berthet, Emmanuel Perrey-Debain, Jean-Daniel Chazot, Sylvain Germes
Summary: This paper presents a model reduction technique for efficiently computing the frequency response functions of damped structures. The frequency-dependent complex moduli are approximated using the Golla-Hughes-MacTavish (GHM) model, which transforms the original problem into a second-order, constant-coefficient system of equations. The matrix system is then treated using the Balanced Proper Orthogonal Decomposition (BPOD) to approximate the transfer function matrix or admittance matrix. The reduction strategy is shown to be efficient in terms of data reduction, accuracy, and computational cost.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2023)
Article
Computer Science, Artificial Intelligence
Yan-Ru Guo, Yan-Qin Bai, Chun-Na Li, Lan Bai, Yuan-Hai Shao
Summary: The paper introduces a novel two-dimensional Bhattacharyya bound linear discriminant analysis method (2DBLDA), which can effectively improve recognition accuracy when handling two-dimensional input samples and avoids the small sample size problem.
APPLIED INTELLIGENCE
(2022)
Article
Mathematics
Amine N. Chakhchoukh, Mark R. Opmeer
INTEGRAL EQUATIONS AND OPERATOR THEORY
(2016)
Article
Mathematics, Applied
Arash Massoudi, Mark R. Opmeer, Timo Reis
NUMERISCHE MATHEMATIK
(2017)
Article
Mathematics, Applied
Arash Massoudi, Mark R. Opmeer, Timo Reis
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
(2016)
Article
Automation & Control Systems
C. Guiver, H. Logemann, M. R. Opmeer
MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS
(2017)
Article
Automation & Control Systems
Mark R. Opmeer
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2012)
Article
Mathematics, Applied
Chris Guiver, Mark R. Opmeer
LINEAR ALGEBRA AND ITS APPLICATIONS
(2013)
Article
Automation & Control Systems
Mark R. Opmeer, Timo Reis, Winnifried Wollner
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2013)
Article
Automation & Control Systems
Chris Guiver, Mark R. Opmeer
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2014)
Article
Automation & Control Systems
Mark R. Opmeer, Olof J. Staffans
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2014)
Article
Mathematics, Applied
Chris Guiver, Mark R. Opmeer
MATHEMATICAL CONTROL AND RELATED FIELDS
(2013)
Article
Automation & Control Systems
Chris Cuiver, Hartmut Logemann, Mark R. Opmeer
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2019)
Article
Automation & Control Systems
Mark R. Opmeer
SYSTEMS & CONTROL LETTERS
(2020)
Proceedings Paper
Automation & Control Systems
Mark R. Opmeer
Summary: This study demonstrates that the ADI method converges exponentially in the square root for a certain class of infinite-dimensional Lyapunov equations with appropriately chosen shift parameters. The main assumption is that the main operator generates an analytic semigroup. Instead of directly analyzing the ADI algorithm, the study focuses on the error estimation through applying quadrature to the inverse Laplace transform integral of the output map.
Article
Automation & Control Systems
Mark R. Opmeer, Olof J. Staffans
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2019)
