相关论文: Inexact Linear Solves In Model Reduction of Biline…
This paper considers large-scale linear stochastic systems representing, e.g., spatially discretized stochastic partial differential equations. Since asymptotic stability can often not be ensured in such a stochastic setting (e.g. due to…
Bilinear matrix inequality (BMI) problems in system and control designs are investigated in this paper. A solution method of reduction of variables (MRVs) is proposed. This method consists of a principle of variable classification, a…
During the past decade, Model Order Reduction (MOR) has become key enabler for the efficient simulation of large circuit models. MOR techniques based on moment-matching are well established due to their simplicity and computational…
We present a method that connects a well-established nonlinear (bilinear) identification method from time-domain data with neural network (NNs) advantages. The main challenge for fitting bilinear systems is the accurate recovery of the…
This paper investigates structure-preserving $H_2$-optimal model order reduction (MOR) for linear systems with quadratic outputs. Within a Petrov-Galerkin projection framework, the $H_2$-optimal MOR problem is first formulated as an…
This paper addresses the problem of asymptotic tracking for high-order control-affine MIMO nonlinear systems with unknown dynamic terms subject to input and transient state constraints. We introduce Barrier Integral Control (BRIC), a novel…
The Iterative Rational Krylov Algorithm (IRKA) of [8] is an interpolatory model reduction approach to the optimal $\mathcal{H}_2$ approximation problem. Even though the method has been illustrated to show rapid convergence in various…
Model Order Reduction (MOR) can significantly reduce the computational cost of vibroacoustic simulations. While most MOR research focuses on single-domain systems (e.g., structural dynamics or computational fluid mechanics), this work…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. Two…
A trained-based Born iterative method (TBIM) is developed for electromagnetic imaging (EMI) applications. The proposed TBIM consists of a nested loop; the outer loop executes TBIM iteration steps, while the inner loop executes a trained…
The bilinear form of a matrix function, namely $\mathbf{u}^\top f(A) \mathbf{v}$, appears in many scientific computing problems, where $\mathbf{u}, \mathbf{v} \in \mathbb{R}^n$, $A \in \mathbb{R}^{n \times n}$, and $f(z)$ is a given…
Optimal stopping is a fundamental class of stochastic dynamic optimization problems with numerous applications in finance and operations management. We introduce a new approach for solving computationally-demanding stochastic optimal…
Science and engineering problems frequently require solving a sequence of dual linear systems. Besides having to store only few Lanczos vectors, using the BiConjugate Gradient method (BiCG) to solve dual linear systems has advantages for…
The purpose of this paper is to introduce a new Kirk type iterative algorithm called Kirk multistep iteration and to study its convergence. We also prove some theorems related with the stability results for the Kirk-multistep and Kirk-SP…
This paper investigates the robust stabilisation of a class of fractional-order non-linear systems via fixed-order dynamic output feedback controller in terms of linear matrix inequalities (LMIs). The systematic stabilisation algorithm…
This paper considers a class of bilinear systems with a neural network in the loop. These arise naturally when employing machine learning techniques to approximate general, non-affine in the input, control systems. We propose a controller…
This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…
We study a non-linear statistical inverse learning problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider the widely used Tikhonov regularization (or method of…
Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing…