Stabilization of the linearized water tank system

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This paper deals with the initial value problem for a semilinear wave equation on a bounded domain and solutions are required to vanish on the boundary of this domain. The essential feature of the situation considered here is that the ellipticity of the sp ...

By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...

We address the problem of designing stabilizing control policies for nonlinear systems in discrete-time, while minimizing an arbitrary cost function. When the system is linear and the cost is convex, the System Level Synthesis (SLS) approach offers an effe ...

Explicit time integration schemes coupled with Galerkin discretizations of time-dependent partial differential equations require solving a linear system with the mass matrix at each time step. For applications in structural dynamics, the solution of the li ...

This paper summarizes a series of analytical studies that were conducted in connection with an improved approach for the design of acceleration-sensitive nonstructural elements. In the new approach, bracing to secure nonstructural elements to the structure ...

The non-dimensional energy of starting vortex rings typically converges to values around 0.33 when they are created by a piston-cylinder or a bluff body translating at a constant speed. To explore the limits of the universality of this value and to analyse ...

Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...

The discretization of robust quadratic optimal control problems under uncertainty using the finite element method and the stochastic collocation method leads to large saddle-point systems, which are fully coupled across the random realizations. Despite its ...

Motivated by the seismic response of unanchored liquid storage tanks, their uplift mechanism under strong lateral loading is examined. Using three-dimensional finite element models, nonlinear static analysis is conducted to define the moment-rotation relat ...

The optimal time for the controllability of linear hyperbolic systems in one dimensional space with one-side controls has been obtained recently for time-independent coefficients in our previous works. In this paper, we consider linear hyperbolic systems w ...

Acceleration measurements are fundamental in applications such as consumer electronics, navigation, automotive safety and Internet of things (IoT). In comparison with capacitive or piezoresistive MEMS accelerometers, resonant graphene accelerometers have t ...

We propose a principled method for projecting an arbitrary square matrix to the non- convex set of asymptotically stable matrices. Leveraging ideas from large deviations theory, we show that this projection is optimal in an information-theoretic sense and ...

Training deep neural networks (DNNs) can be difficult due to the occurrence of vanishing/explod- ing gradients during weight optimization. To avoid this problem, we propose a class of DNNs stemming from the time discretization of Hamiltonian systems. The t ...

In this paper, we discuss our recent works on the null-controllability, the exact controllability, and the stabilization of linear hyperbolic systems in one dimensional space using boundary controls on one side for the optimal time. Under precise and gener ...

Enabling analysis of non-linear systems in linear form, the Koopman operator has been shown to be a powerful tool for system identification and controller design. However, current data-driven methods cannot provide quantification of model uncertainty given ...

We consider the finite-time stabilization of homogeneous quasilinear hyperbolic systems with one side controls and with nonlinear boundary condition at the other side. We present time-independent feedbacks leading to the finite-time stabilization in any ti ...

When laminar shear flows in large wall-bounded domains transition to turbulence, the flow exhibits spatio-temporally chaotic dynamics. Despite its chaotic dynamics, the flow may self-organize into characteristic spatially periodic patterns of unknown origi ...

Linear matrix equations, such as the Sylvester and Lyapunov equations, play an important role in various applications, including the stability analysis and dimensionality reduction of linear dynamical control systems and the solution of partial differentia ...

The extensive use of frequency-domain tools for analyzing and controlling linear systems have become indispensable for the control systems engineer. However, due to the increased performance demands on today's industrial systems, the effects of certain non ...

PURPOSE: To investigate the effect of spatial resolution and parallel imaging acceleration factor on the quality of the motion estimates derived from image navigators with a three-dimensional (3D) gradient-recalled echo (GRE) acquisition with fat excitatio ...

Stabilization of the linearized water tank system

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Critical degeneracy in a nonlinear hyperbolic equation can produce atypical instability

Additive and geometric transversality of fractal sets in the integers

Neural System Level Synthesis: Learning over All Stabilizing Policies for Nonlinear Systems

A mathematical theory for mass lumping and its generalization with applications to isogeometric analysis

Analytical Studies in Support of an Improved Approach to the Design of Acceleration-Sensitive Nonstructural Elements

Estimating the non-dimensional energy of vortex rings by modelling their roll-up

Fourier non-uniqueness sets from totally real number fields

Preconditioners for robust optimal control problems under uncertainty

Uplift mechanics of unanchored liquid storage tanks subjected to lateral earthquake loading

On the optimal controllability time for linear hyperbolic systems with time-dependent coefficients

Proof Of Concept Of A Graphene-Based Resonant Accelerometer

Efficient Learning of a Linear Dynamical System with Stability Guarantees

A unified framework for Hamiltonian deep neural networks

Null-controllability, exact controllability, and stabilization of hyperbolic systems for the optimal time

On Gaussian Process Based Koopman Operators

Finite-time stabilization in optimal time of homogeneous quasilinear hyperbolic systems in one dimensional space

Turbulent patterns in wall-bounded shear flows: invariant solutions and their bifurcations

Low-Rank Updates And A Divide-And-Conquer Method For Linear Matrix Equations

Robust Controller Design For Linear Systems With Nonlinear Distortions: A Data-Driven Approach

Optimizing the acceleration and resolution of three-dimensional fat image navigators for high-resolution motion correction at 7T