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The relative degree limitation for adaptive observer-based synchronization schemes is overcome. The scheme is extended to nonpassifiable systems. Two synchronization methods are described and justified based on augmented error adaptive…

Optimization and Control · Mathematics 2007-05-23 V. O. Nikiforov , A. L. Fradkov , B. R. Andrievsky

We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze…

Image and Video Processing · Electrical Eng. & Systems 2024-07-10 Mehrsa Pourya , Sebastian Neumayer , Michael Unser

We consider the effect of using approximate system predictions in event-triggered control schemes. Such approximations may result from using numerical transcription methods for solving continuous-time optimal control problems. Mesh…

Systems and Control · Electrical Eng. & Systems 2021-05-31 Omar J. Faqir , Eric C. Kerrigan

This work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator mapping arbitrary nodal values into bound-preserving ones…

Numerical Analysis · Mathematics 2023-04-04 Gabriel Barrenechea , Emmanuil Georgoulis , Tristan Pryer , Andreas Veeser

We consider linear iterative schemes for the time-discrete equations stemming from a class of nonlinear, doubly-degenerate parabolic equations. More precisely, the diffusion is nonlinear and may vanish or become multivalued for certain…

Numerical Analysis · Mathematics 2025-08-12 Ayesha Javed , Koondanibha Mitra , Iuliu Sorin Pop

While it is well known that nonlinear methods of approximation can often perform dramatically better than linear methods, there are still questions on how to measure the optimal performance possible for such methods. This paper studies…

Numerical Analysis · Mathematics 2020-09-22 Albert Cohen , Ronald DeVore , Guergana Petrova , Przemyslaw Wojtaszczyk

Lattice-Boltzmann methods are known for their simplicity, efficiency and ease of parallelization, usually relying on uniform Cartesian meshes with a strong bond between spatial and temporal discretization. This fact complicates the crucial…

Numerical Analysis · Mathematics 2022-10-19 Thomas Bellotti , Loïc Gouarin , Benjamin Graille , Marc Massot

Explicit stabilized methods are highly efficient time integrators for large and stiff systems of ordinary differential equations especially when applied to semi-discrete parabolic problems. However, when local spatial mesh refinement is…

Numerical Analysis · Mathematics 2025-10-20 Mathieu Benninghoff , Gilles Vilmart

In this paper, we present a robust adaptive model predictive control (MPC) scheme for linear systems subject to parametric uncertainty and additive disturbances. The proposed approach provides a computationally efficient formulation with…

Systems and Control · Electrical Eng. & Systems 2020-03-12 Johannes Köhler , Elisa Andina , Raffaele Soloperto , Matthias A. Müller , Frank Allgöwer

This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…

Numerical Analysis · Mathematics 2025-05-07 Xu Wu , Jiang Yang , Zhi Zhou

Lattice Boltzmann Methods (LBM) stand out for their simplicity and computational efficiency while offering the possibility of simulating complex phenomena. While they are optimal for Cartesian meshes, adapted meshes have traditionally been…

Numerical Analysis · Mathematics 2022-02-28 Loïc Gouarin , Benjamin Graille , Marc Massot , Thomas Bellotti

Strength-of-connection algorithms play a key role in algebraic multigrid (AMG). Specifically, they determine which matrix nonzeros are classified as weak and so ignored when coarsening matrix graphs and defining interpolation sparsity…

Numerical Analysis · Mathematics 2026-04-16 Chris Siefert , Raymond Tuminaro , Daniel Sunderland

This paper is concerned with adaptive mesh refinement strategies for the spatial discretization of parabolic problems with dynamic boundary conditions. This includes the characterization of inf-sup stable discretization schemes for a…

Numerical Analysis · Mathematics 2023-10-12 Robert Altmann , Christoph Zimmer

Curvilinear, multiblock summation-by-parts finite difference operators with the simultaneous approximation term method provide a stable and accurate framework for solving the wave equation in second order form. That said, the standard…

Numerical Analysis · Mathematics 2022-09-07 Brittany A Erickson , Jeremy E Kozdon , Tobias W Harvey

We prove new optimality results for adaptive mesh refinement algorithms for non-symmetric, indefinite, and time-dependent problems by proposing a generalization of quasi-orthogonality which follows directly from the inf-sup stability of the…

Numerical Analysis · Mathematics 2022-03-22 Michael Feischl

This paper develops a quantitative framework for analyzing the mean-square exponential stabilization of stochastic linear systems with multiplicative noise, focusing specifically on the optimal stabilizing rate, which characterizes the…

Optimization and Control · Mathematics 2025-12-15 Hui Jia , Yuan-Hua Ni , Guangchen Wang

We report on the development of a computational framework for the parallel, mesh-adaptive solution of systems of hyperbolic conservation laws like the time-dependent Euler equations in compressible gas dynamics or Magneto-Hydrodynamics…

Computational Physics · Physics 2007-05-23 J. Dreher , R. Grauer

This paper aims to study the convergence of adaptive finite element method for control constrained elliptic optimal control problems under $L^2$-norm. We prove the contraction property and quasi-optimal complexity for the $L^2$-norm errors…

Numerical Analysis · Mathematics 2016-11-16 Wei Gong , Ningning Yan , Zhaojie Zhou

We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently…

Dynamical Systems · Mathematics 2023-02-07 Dan Wilson , Kai Sun

This paper presents extensions of finite-time stability results to some prototypical adaptive control and estimation frameworks. First, we present a novel scheme of online parameter estimation that guarantees convergence of the estimation…

Optimization and Control · Mathematics 2020-10-20 Kunal Garg , Parag Bobade , Dimitra Panagou