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Motion planning and control are two core components of the robotic systems autonomy stack. The standard approach to combine these methodologies comprises an offline/open-loop stage, planning, that designs a feasible and safe trajectory to…
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…
How is it possible to read the dynamical properties (ie when the time goes to infinity) of a system on numerical simulations? To try to answer this question, we study in this manuscript a model reflecting what happens when the orbits of a…
This article is concerned with the numerical solution of subspace optimization problems, consisting of minimizing a smooth functional over the set of orthogonal projectors of fixed rank. Such problems are encountered in particular in…
Numerical solutions of partial differential equations enable a broad range of scientific research. The Dedalus Project is a flexible, open-source, parallelized computational framework for solving general partial differential equations using…
This paper presents a unified framework to tackle estimation problems in Digital Signal Processing (DSP) using Support Vector Machines (SVMs). The use of SVMs in estimation problems has been traditionally limited to its mere use as a…
Fractional derivative relaxation type equations (FREs) including fractional diffusion equation and fractional relaxation equation, have been widely used to describe anomalous phenomena in physics. To utilize the characteristics of…
We consider numerical schemes for computing the linear response of steady-state averages of stochastic dynamics with respect to a perturbation of the drift part of the stochastic differential equation. The schemes are based on Girsanov's…
A second order accurate, linear numerical method is analyzed for the Landau-Lifshitz equation with large damping parameters. This equation describes the dynamics of magnetization, with a non-convexity constraint of unit length of the…
This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups…
This paper introduces a method for efficiently updating a nominal stabilizing static output feedback (SOF) controller in perturbed linear systems. As operating points and state-space matrices change in dynamic systems, accommodating updates…
Signal Temporal Logic (STL) has gained popularity in recent years as a specification language for cyber-physical systems, especially in robotics. Beyond being expressive and easy to understand, STL is appealing because the synthesis…
Long-term time series forecasting (LTSF) is a challenging task that has been investigated in various domains such as finance investment, health care, traffic, and weather forecasting. In recent years, Linear-based LTSF models showed better…
A typical procedure to integrate numerically the time dependent Schr\"o\-din\-ger equation involves two stages. In the first one carries out a space discretization of the continuous problem. This results in the linear system of differential…
Stochastic switched systems are a relevant class of stochastic hybrid systems with probabilistic evolution over a continuous domain and control-dependent discrete dynamics over a finite set of modes. In the past few years several different…
In this paper, we study a numerical method for the solution of partial differential equations on evolving surfaces. The numerical method is built on the stabilized trace finite element method (TraceFEM) for the spatial discretization and…
This paper investigates a numerical probabilistic method for the solution of some semilinear stochastic partial differential equations (SPDEs in short). The numerical scheme is based on discrete time approximation for solutions of systems…
Crack microgeometries pose a paramount influence on effective elastic characteristics and sonic responses. Geophysical exploration based on seismic methods are widely used to assess and understand the presence of fractures. Numerical…
The problem of the logarithmic discretization of an arbitrary positive function (such as the density of states) is studied in general terms. Logarithmic discretization has arbitrary high resolution around some chosen point (such as Fermi…
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain…