Related papers: Numerical modelling of coupled linear dynamical sy…
Coupled partial differential equations defined on domains with different dimensionality are usually called mixed dimensional PDEs. We address mixed dimensional PDEs on three-dimensional (3D) and one-dimensional domains, giving rise to a…
Coupled-bunch instabilities excited by the interaction of the particle beam with its surroundings can seriously limit the performance of circular particle accelerators. These instabilities can be cured by the use of active feedback systems…
The evolution of images with physics-based dynamics is often spatially localized and nonlinear. A switching linear dynamic system (SLDS) is a natural model under which to pose such problems when the system's evolution randomly switches over…
The paper considers a coupled system of linear Boltzmann transport equations (BTE), and its Continuous Slowing Down Approximation (CSDA). This system can be used to model the relevant transport of particles used e.g. in dose calculation in…
Many physical problems involving heterogeneous spatial scales, such as the flow through fractured porous media, the study of fiber-reinforced materials, or the modeling of the small circulation in living tissues -- just to mention a few…
We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical…
Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…
We consider the problem of learning a realization of a partially observed bilinear dynamical system (BLDS) from noisy input-output data. Given a single trajectory of input-output samples, we provide a finite time analysis for learning the…
In this paper, the problem of placing sensors for some classes of nonlinear dynamic systems (NDS) is investigated. In conjunction with mixed-integer programming, classical Lyapunov-based arguments are used to find the minimal sensor…
We use direct statistical simulation (DSS) to find the low-order statistics of the well-known dynamical system, the Lorenz63 model. Instead of accumulating statistics from numerical simulation of the dynamical systems, we solve the…
Stability of power networks is an increasingly important topic because of the high penetration of renewable distributed generation units. This requires the development of advanced (typically model-based) techniques for the analysis and…
A method of expansion of solutions of singularly perturbed nonlinear systems in power series of small parameters is applied to the popular Lorenz model in synergetics.Simple asymptotic expressions for the solution to the model in…
Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning multivariate time series. However, in general, it is difficult to set the dimension of its hidden state space. A small number of hidden states may…
Distributed parameter systems (DPS) are formulated as partial differential equations (PDE). Especially, under time-varying boundary conditions, PDE introduce force coupling. In the case of the flexible stacker crane (STC), nonlinear…
With this contribution, we give a complete and comprehensive framework for modeling the dynamics of complex mechanical structures as port-Hamiltonian systems. This is motivated by research on the potential of lightweight construction using…
Many real world systems exhibit a quasi linear or weakly nonlinear behavior during normal operation, and a hard saturation effect for high peaks of the input signal. In this paper, a methodology to identify a parsimonious discrete-time…
Passive systems are characterized by their inability to generate energy internally, providing a powerful tool for modeling physical phenomena. Additionally, algebraically encoding passivity in the system description can be advantageous. For…
A new linear relaxation system for nonconservative hyperbolic systems is introduced, in which a nonlocal source term accounts for the nonconservative product of the original system. Using an asymptotic analysis the relaxation limit and its…
This paper addresses the numerical optimization of proportional-integral-derivative (PID) controllers for linear time-invariant systems with delays, where the derivative action is implemented using a low-pass filter. While performance…
Neural population activity exhibits complex, nonlinear dynamics, varying in time, over trials, and across experimental conditions. Here, we develop Conditionally Linear Dynamical System (CLDS) models as a general-purpose method to…