Related papers: Nonlinear balanced truncation model reduction thro…
Structured reduced-order modeling is a central component in the computer-aided design of control systems in which cheap-to-evaluate low-dimensional models with physically meaningful internal structures are computed. In this work, we develop…
We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…
Nonlinear state-space modelling is a very powerful black-box modelling approach. However powerful, the resulting models tend to be complex, described by a large number of parameters. In many cases interpretability is preferred over…
We develop a pivot-shifted Carleman linearization framework for quantum algorithms solving quadratic nonlinear ordinary differential equations. By shifting the dynamics by a pivot state prior to Carleman lifting, and combining this with a…
A systematic approach to nonlinear model order reduction (NMOR) of coupled fluid-structureflight dynamics systems of arbitrary fidelity is presented. The technique employs a Taylor series expansion of the nonlinear residual around…
Kernel approximation with exponentials is useful in many problems with convolution quadrature and particle interactions such as integral-differential equations, molecular dynamics and machine learning. This paper proposes a weighted…
This paper presents a structure-exploiting nonlinear model reduction method for systems with general nonlinearities. First, the nonlinear model is lifted to a model with more structure via variable transformations and the introduction of…
This article surveys nonlinear model reduction methods that remain effective in regimes where linear reduced-space approximations are intrinsically inefficient, such as transport-dominated problems with wave-like phenomena and moving…
In this paper, we aim at developing computationally tractable methods for nonlinear model/controller reduction. Recently, model reduction by generalized differential (GD) balancing has been proposed for nonlinear systems with constant…
Small signal analysis is a special case of analytical approaches using Taylor expansions of power system differential equations with the truncation performed at order one. The truncated Taylor expansions (TTEs) at higher orders can lead to…
We consider the problem of constructing reduced models for large scale systems with poles in general domains in the complex plane (as opposed to, e.g., the open left-half plane or the open unit disk). Our goal is to design a model reduction…
In this paper, we propose a new approach to design globally convergent reduced-order observers for nonlinear control systems via contraction analysis and convex optimization. Despite the fact that contraction is a concept naturally suitable…
This paper studies the data-driven balanced truncation (BT) method for second-order systems based on the measurements in the frequency domain. The basic idea is to approximate Gramians used the numerical quadrature rules, and establish the…
Nonlinear control allocation is an important part of modern nonlinear dynamic inversion based flight control systems which require highly accurate model of aircraft aerodynamics. Generally, an accurately implemented onboard model determines…
Balanced truncation is one of the most common model order reduction schemes. In this paper, we study finite-frequency model order reduction (FF-MOR) problems of linear continuous-time systems within the framework of balanced truncation…
We study filtering of multiscale dynamical systems with model error arising from unresolved smaller scale processes. The analysis assumes continuous-time noisy observations of all components of the slow variables alone. For a linear model…
Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results…
This paper discusses model order reduction of LTI systems over limited frequency intervals within the framework of balanced truncation. Two new \emph{frequency-dependent balanced truncation} methods were developed, one is \emph{SF-type…
The problem of controller reduction has a rich history in control theory. Yet, many questions remain open. In particular, there exist very few results on the order reduction of general non-observer based controllers and the subsequent…
The Harmonic Balance method provides a heuristic approach for finding truncated Fourier series as an approximation to the periodic solutions of ordinary differential equations. Another natural way for obtaining these type of approximations…