Related papers: Virtual Testing of Experimental Continuation
An experimental method has been developed to locate unstable equilibria of nonlinear structures quasi-statically. The technique involves loading a structure by application of either a force or a displacement at a main actuation point, while…
Experimental continuation encompasses a set of methods that combine control and continuation to obtain the full bifurcation diagram of a nonlinear system experimentally, including responses that would be unstable in the system without…
This paper presents a framework to perform bifurcation analysis in laboratory experiments or simulations. We employ control-based continuation to study the dynamics of a macroscopic variable of a microscopically defined model, exploring the…
We present and analyze a structure-preserving method for the approximation of solutions to nonlinear cross-diffusion systems, which combines a Local Discontinuous Galerkin spatial discretization with the backward Euler time-stepping scheme.…
Control-based continuation is technique for tracking the solutions and bifurcations of nonlinear experiments. The basic idea is to apply the method of numerical continuation to a feedback-controlled physical experiment. Since in an…
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by…
Real-time hybrid testing is a method in which a substructure of the system is realised experimentally and the rest numerically. The two parts interact in real time to emulate the dynamics of the full system. Such experiments however are…
We present and analyze a discontinuous Galerkin method for the numerical modeling of a Kelvin-Voigt thermo/poro-viscoelastic problem. We present the derivation of the model and we develop a stability analysis in the continuous setting that…
We propose and rigorously analyse semi- and fully discrete discontinuous Galerkin methods for an initial and boundary value problem describing inertial viscoelasticity in terms of elastic and viscoelastic stress components, and with mixed…
A mixed continuous / discontinuous Galerkin scheme is introduced for the simulation of fluid-structure interaction problems in an isogeometric analysis framework. The properties of Non-Uniform Rational B-Spline basis functions are leveraged…
In uncertainty quantification, critical parameters of mathematical models are substituted by random variables. We consider dynamical systems composed of ordinary differential equations. The unknown solution is expanded into an orthogonal…
In this paper, we investigate the null controllability of nonlinear wave systems. Initially, we employ a combination of the Galerkin method and a fixed point theorem to establish the null controllability for semi-linear wave equations with…
In the research community, there exists the strong belief that a continuous Galerkin scheme is notoriously unstable and additional stabilization terms have to be added to guarantee stability. In the first part of the series [6], the…
In this paper, we introduce a novel high-order shock tracking method and provide a proof of concept. Our method leverages concepts from implicit shock tracking and extended discontinuous Galerkin methods, primarily designed for solving…
An approach to stabilization of control systems with ultimately wide ranges of uncertainly disturbed parameters is offered. The method relies on using of nonlinear structurally stable functions from catastrophe theory as controllers.…
A methodology for handling block-to-block coupling of nonconforming, multiblock summation-by-parts finite difference methods is proposed. The coupling is based on the construction of projection operators that move a finite difference grid…
In this paper, we address the problem of stabilizing a system around a desired manifold determined by virtual nonlinear nonholonomic constraints. Virtual constraints are relationships imposed on a control system that are rendered invariant…
This paper proposes a constructive approach to safety control of nonlinear cascade systems subject to multiple state constraints. New design ingredients include a unified characterization of safety and stability for systematic designs of…
Standard geometric control relies on force-moment decoupling, an assumption that breaks down in many aerial platforms due to spurious forces naturally induced by control moments. While strategies for such coupled systems have been validated…
Nonlinear dynamics of fluid conveying pipe, rotating with constant velocity about its longitudinal axis is analyzed. Considering boundary conditions and internal damping, the nonlinear equation of motion is derived, and it is discretized…