Related papers: Order Reduction of Nonlinear Quasi-periodic System…
This paper presents an efficient algorithm for robust network reconstruction of Linear Time-Invariant (LTI) systems in the presence of noise, estimation errors and unmodelled nonlinearities. The method here builds on previous work on robust…
This paper deals with the problem of robust dynamic output feedback stabilization of interval fractional-order linear time invariant (FO-LTI) systems with the fractional order $1\le\alpha<2$. In this study, a new formulation based on the…
The low-rank alternating directions implicit (LR-ADI) iteration is a frequently employed method for efficiently computing low-rank approximate solutions of large-scale Lyapunov equations. In order to achieve a rapid error reduction, the…
With the increasing penetration of distributed energy resources (DERs), it is of vital importance to study the dynamic stability of microgrids (MGs) with external control inputs in the electromagnetic transient (EMT) time scale. This…
The objective of this contribution is to compare two methods proposed recently in order to build efficient reduced-order models for geometrically nonlinear structures. The first method relies on the normal form theory that allows one to…
In the framework of KAM theory, the persistence of invariant tori in quasi-integrable systems is proved by assuming a non-resonance condition on the frequencies, such as the standard Diophantine condition or the milder Bryuno condition. In…
It is well known that Lawson methods suffer from a severe order reduction when integrating initial boundary value problems where the solutions are not periodic in space or do not satisfy enough conditions of annihilation on the boundary.…
A reduced-order model algorithm, called ALP, is proposed to solve nonlinear evolution partial differential equations. It is based on approximations of generalized Lax pairs. Contrary to other reduced-order methods, like Proper Orthogonal…
We present a finite-time framework for identifying stable and unstable linear time-invariant (LTI) systems from a single closed-loop input-output trajectory. The method does not require knowledge of the stabilizing controller, an…
Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…
In this paper, a practicable simulation-free model order reduction method by nonlinear moment matching is developed. Based on the steady-state interpretation of linear moment matching, we comprehensively explain the extension of this…
We propose a computationally efficient framework to treat nonlinear partial differential equations having bifurcating solutions as one or more physical control parameters are varied. Our focus is on steady bifurcations. Plotting a…
We provide new insights into the a priori theory for a time-stepping scheme based on least-squares finite element methods for parabolic first-order systems. The elliptic part of the problem is of general reaction-convection-diffusion type.…
In this paper, a computationally efficient frequency-limited model reduction algorithm is presented for large-scale interconnected power systems. The algorithm generates a reduced order model which not only preserves the electromechanical…
We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system…
Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves.…
This serial work presents a Linear-Time-Invariance (LTI) notion to the Koopman analysis, finding consistent and physically meaningful Koopman modes and addressing a long-standing problem of fluid-structure interactions: deterministically…
Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…
We present here the details of a backstepping transformation aiming at reformulating the dynamics of a nonlinear systems subject to unknown long input delay in a form which is suitable for Lyapunov stability analysis. The control law…
This paper presents a novel approach for the identification of linear time-periodic (LTP) systems in continuous time. This method is based on harmonic modeling and consists in converting any LTP system into an equivalent LTI system with…