Related papers: A non-damped stabilization algorithm for multibody…
We consider the question of determining whether or not a given system of fractional-order differential equations is (asymptotically) stable. In particular, we admit systems where each constituent equation may have its own order, independent…
In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and…
Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…
Harmonic Balance is one of the most popular methods for computing periodic solutions of nonlinear dynamical systems. In this work, we address two of its major shortcomings: First, we investigate to what extent the computational burden of…
The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time-delay systems, an exact stability result is firstly derived…
We present a structure-preserving scheme based on a recently-proposed mixed formulation for incompressible hyperelasticity formulated in principal stretches. Although there exist Hamiltonians introduced for quasi-incompressible…
Despite the advancements in learning governing differential equations from observations of dynamical systems, data-driven methods are often unaware of fundamental physical laws, such as frame invariance. As a result, these algorithms may…
The purpose of this paper is twofold. An immediate practical use of the presented algorithm is its applicability to the parametric solution of underdetermined linear ordinary differential equations (ODEs) with coefficients that are…
This article emphasizes on inconsistencies in the dynamical estimates obtained by first-order transverse discontinuity mapping (TDM) and direct numerical observations for hybrid dynamical systems. Pitfalls of locally linearizing hybrid…
In this work we propose and analyze a novel Hybrid High-Order discretization of a class of (linear and) nonlinear elasticity models in the small deformation regime which are of common use in solid mechanics. The proposed method is valid in…
This work concerns the internal stabilization of underactuated linear systems of $m$ heat equations in cascade, where the control is placed internally in the first equation only and the diffusion coefficients are distinct. Combining the…
We introduce the notion of descriptor embedding for nonlinear systems and use it for the data-driven design of stabilizing controllers. Specifically, we provide sufficient data-dependent LMI conditions which, if feasible, return a…
This article proposes a novel methodology to learn a stable robot control law driven by dynamical systems. The methodology requires a single demonstration and can deduce a stable dynamics in arbitrary high dimensions. The method relies on…
Differential algebraic equations (DAEs) describe the temporal evolution of systems that obey both differential and algebraic constraints. Of particular interest are systems that contain implicit relationships between their components, such…
In this paper, we introduce some new hybrid algorithms for finding a solution of a system of equilibrium problems. In these algorithms, by constructing specially cutting-halfspaces, we avoid using the extra-steps as in the extragradient…
We consider spectral discretizations of hyperbolic problems on unbounded domains using Laguerre basis functions. Taking as model problem the scalar advection equation, we perform a comprehensive stability analysis that includes strong…
Dynamic state estimation (DSE) is becoming increasingly important for monitoring inverter-dominated power systems. Due to their cascading control structures, inverter-based resources (IBRs) exhibit multi-timescale dynamics, leading to stiff…
Optimal sensor placement is essential for minimizing costs and ensuring accurate state estimation in power systems. This paper introduces a novel method for optimal sensor placement for dynamic state estimation of power systems modeled by…
This paper investigates two optimization criteria for damping optimization in a multi-body oscillator system with arbitrary degrees of freedom ($n$), resembling string/rod free vibrations. The total average energy over all possible initial…
The fastest known algorithms for dealing with structured matrices, in the sense of the displacement rank measure, are randomized. For handling classical displacement structures, they achieve the complexity bounds…