Related papers: Integral Equations & Model Reduction For Fast Comp…
This paper transfers the concept of moment matching to nonlinear structural systems and further provides a simulation-free reduction scheme for such nonlinear second-order models. After first presenting the steady-state interpretation of…
We study the acceleration of steady-state computation for microflow, which is modeled by the high-order moment models derived recently from the steady-state Boltzmann equation with BGK-type collision term. By using the lower-order model…
Simulations of the dynamics generated by partial differential equations (PDEs) provide approximate, numerical solutions to initial value problems. Such simulations are ubiquitous in scientific computing, but the correctness of the results…
We show how the solution to NMPC problems for a special type of input-affine discrete-time systems can be obtained by reformulating the underlying non-convex optimal control problem in terms of a finite number of convex subproblems. The…
Invariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems, for instance, spectral submanifolds have emerged as useful…
Convolution-type integral equations arise from various fields, \textit{e.g.}, finite impulse response filters in signal processing and deblurring problems in image processing. When solving these equations, conventional numerical methods,…
This paper describes an adaptive method to reduce a nonlinear power system model for fast and accurate transient stability simulation. It presents an approach to analyze and rank participation factors of each system state variable into…
A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the…
This paper addresses the problem of robust process and sensor fault reconstruction for nonlinear systems. The proposed method augments the system dynamics with an approximated internal linear model of the combined contribution of known…
We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases. The approach relies on an offline computation of a dictionary of solutions together with an online…
In this paper, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating nonlinearities onto approximation spaces defined with the help of finite elements, the…
This paper presents a model predictive control (MPC) for dynamic systems whose nonlinearity and uncertainty are modelled by deep neural networks (NNs), under input and state constraints. Since the NN output contains a high-order complex…
In this paper, we introduce an iterative numerical method to solve systems of nonlinear equations. The third-order convergence of this method is analyzed. Several examples are given to illustrate the efficiency of the proposed method.
We present an efficient variational integrator for multibody systems. Variational integrators reformulate the equations of motion for multibody systems as discrete Euler-Lagrange (DEL) equations, transforming forward integration into a…
This work studies the design problem of feedback stabilizers for discrete-time systems with input delays. A backstepping procedure is proposed for disturbance-free discrete-time systems. The feedback law designed by using backstepping…
This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form…
We consider the problem of reconstructing signals and images from periodic nonlinearities. For such problems, we design a measurement scheme that supports efficient reconstruction; moreover, our method can be adapted to extend to…
This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based…
We provide a solution to the heretofore open problem of stabilization of systems with arbitrarily long delays at the input and output of a nonlinear system using output feedback only. The solution is global, employs the predictor approach…
The design of structures submitted to aerodynamic loads usually requires the development of specific computational models considering fluid-structure interactions. Models using structural frame elements are developed in several relevant…