相关论文: Geometric analysis of nonlinear differential-algeb…
Using dual perturbation theory in a non-sun-reflexive context, we establish a correspondence between 1. a class of nonlinear abstract delay differential equations (DDEs) with unbounded linear part and an unknown taking values in an…
A class of two-dimensional globally scale-invariant, but not conformally invariant, theories is obtained. These systems are identified in the process of discussing global and local scaling properties of models related by duality…
Nonlinear operators with long distance spatiotemporal dependencies are fundamental in modeling complex systems across sciences, yet learning these nonlocal operators remains challenging in machine learning. Integral equations (IEs), which…
Modern modeling languages for general physical systems, such as Modelica, Amesim, or Simscape, rely on Differential Algebraic Equations (DAE), i.e., constraints of the form f(dot{x},x,u)=0. This drastically facilitates modeling from first…
Multirate behavior of ordinary differential equations (ODEs) and differential-algebraic equations (DAEs) is characterized by widely separated time constants in different components of the solution or different additive terms of the…
Solutions to most nonlinear ordinary differential equations (ODEs) rely on numerical solvers, but this gives little insight into the nature of the trajectories and is relatively expensive to compute. In this paper, we derive analytic…
Neural ordinary differential equations (Neural ODEs) define continuous time dynamical systems with neural networks. The interest in their application for modelling has sparked recently, spanning hybrid system identification problems and…
We establish the dual notions of scaling and saturation from geometric control theory in an infinite-dimensional setting. This generalization is applied to the low-mode control problem in a number of concrete nonlinear partial differential…
We study the application of generalized symmetry for reducing nonlinear partial differential equations. We construct the ansatzes for dependent variable $u$ which reduce the scalar partial differential equation with two independent…
A new category of Lie algebras, called generalized Lie algebras, is presented such that classical Lie algebras and Lie-Rinehart algebras are objects of this new category. A new philosophy over generalized Lie algebroids theory is presented…
We outline a new geometric method of constructing exact solutions of gravitational field equations parametrized by generic off-diagonal metrics, anholonomic frames and possessing, in general, nontrivial torsion and nonmetricity. The…
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches…
We consider exact and averaged control problem for a system of quasi-linear ODEs and SDEs with a non-negative definite symmetric matrix of the system. The strategy of the proof is the standard linearization of the system by fixing the…
The nonlinear generalized modified Emden type equations (GMEE) are known to be linearizable into simple harmonic oscillator (HO) or damped harmonic oscillators (DHO) via some nonlocal transformations. Hereby, we show that the structure of…
The study of bifurcations of differential-algebraic equations (DAEs) is the topic of interest for many applied sciences, such as electrical engineering, robotics, etc. While some of them were investigated already, the full classification of…
Based on the matrix expression of general nonlinear numerical analogues presented by the present author, this paper proposes a novel philosophy of nonlinear computation and analysis. The nonlinear problems are considered an ill-posed linear…
This is an elementary introduction to exterior differential systems motivated by two examples: minimal submanifolds and the isometric embedding problem. The two main goals of the lectures are: 1. To explain how to find an appropriate…
We analyze Neural Ordinary Differential Equations (NODEs) from a control theoretical perspective to address some of the main properties and paradigms of Deep Learning (DL), in particular, data classification and universal approximation.…
Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic…