相关论文: The invariant manifold approach applied to nonline…

Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…

The performance of machine learning models can be impacted by changes in data over time. A promising approach to address this challenge is invariant learning, with a particular focus on a method known as invariant risk minimization (IRM).…

The paper introduces an interactive machine learning mechanism to process the measurements of an uncertain, nonlinear dynamic process and hence advise an actuation strategy in real-time. For concept demonstration, a trajectory-following…

A general, variational approach to derive low-order reduced systems for nonlinear systems subject to an autonomous forcing, is introduced. The approach is based on the concept of optimal parameterizing manifold (PM) that substitutes the…

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…

We study the dynamical response of a circularly-driven rigid body, focusing on the description of intrinsic rotational behavior (reverse rotations). The model system we address is integrable but nontrivial, allowing for qualitative and…

This paper explores how to identify a reduced order model (ROM) from a physical system. A ROM captures an invariant subset of the observed dynamics. We find that there are four ways a physical system can be related to a mathematical model:…

Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…

Invariant manifolds are the skeleton of the chaotic dynamics in Hamiltonian systems. In Celestial Mechanics, for instance, these geometrical structures are applied to a multitude of physical and practical problems, such as to the…

This paper presents a research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. This paper outlines the stability analysis and a procedure to reduce and simplify the non-linear…

The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we…

In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider a model for spin-orbital motion: orbital…

The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…

This paper describes the use of a quadratic manifold for the model order reduction of structural dynamics problems featuring geometric nonlinearities. The manifold is tangent to a subspace spanned by the most relevant vibration modes, and…

This paper presents a learning-based approach for impromptu trajectory tracking for non-minimum phase systems, i.e., systems with unstable inverse dynamics. Inversion-based feedforward approaches are commonly used for improving tracking…

The main objective of this paper is to propose an alternative procedure to carry out one of the key steps of immersion and invariance stabilising controller design. Namely, the one that ensures attractivity of the manifold whose internal…

An imbalanced rotor is considered. A system of moving balancing masses is given. We determine the optimal movement of the balancing masses to minimize the imbalance on the rotor. The optimal movement is given by an open-loop control solving…

The parametrisation method for invariant manifolds is a powerful technique for deriving reduced-order models in the context of nonlinear vibrating systems, allowing accurate computations of nonlinear normal modes. Thanks to arbitrary order…

We identify reduced order models (ROM) of forced systems from data using invariant foliations. The forcing can be external, parametric, periodic or quasi-periodic. The process has four steps: 1. identify an approximate invariant torus and…

Given a symmetry group one can construct the invariant dynamics using the technique of nonlinear realizations or the orbit method. The relationship between these methods is discussed. Few examples are presented.