Related papers: Non linear system become linear system
The problem of separating structured information representing phenomena of differing natures is considered. A structure is assumed to be independent of the others if can be represented in a complementary subspace. When the concomitant…
We review a possible framework for (non)linear quantum theories, into which linear quantum mechanics fits as well, and discuss the notion of ``equivalence'' in this setting. Finally, we draw the attention to persisting severe problems of…
This article addresses the following problems: 1) First, a nonlinearity analysis is made looking for the presence of nonlinearities in an early phase of the identification process. The level and the nature of the nonlinearities should be…
This paper shows how the theory of nonlinear adaptive observers can be effectively used in the design of internal models for nonlinear output regulation. The theory substantially enhances the existing results in the context of {\em…
A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.
In this article, we discuss some of the recent developments in applying machine learning (ML) techniques to nonlinear dynamical systems. In particular, we demonstrate how to build a suitable ML framework for addressing two specific…
We discuss the possibility of making the {\it initial} definitions of mutually different (possibly interacting, or even entangled) systems in the context of decoherence theory. We point out relativity of the concept of elementary physical…
We present a novel approach for learning nonlinear dynamic models, which leads to a new set of tools capable of solving problems that are otherwise difficult. We provide theory showing this new approach is consistent for models with long…
In this work, we propose novel method for certifying if a given set of vertex linear systems constitute a linear difference inclusion for a nonlinear system. The method relies on formulating the verification of the inclusion as an…
These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…
A novel control design approach for general nonlinear systems is presented in this paper. The approach is based on the identification of a polynomial model of the system to control and on the on-line inversion of this model. An efficient…
Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of…
This is a brief review of recent theoretical efforts to understand persistence in nonequilibrium systems. Some of the recent experimental results are also briefly mentioned. I also discuss recent generalizations of persistence in various…
In this paper we study the existence of solutions to an isotropic differential inclusion.
An analysis of discrete systems is important for understanding of various physical processes, such as excitations in crystal lattices and molecular chains, the light propagation in waveguide arrays, and the dynamics of Bose-condensate…
Nonlinear dynamical systems are widely encountered in various scientific and engineering fields. Despite significant advances in theoretical understanding, developing complete and integrated frameworks for analyzing and designing these…
We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, algebraic statistics, integrable systems, configuration…
Coupling of chaotic oscillators has evidenced conditions where synchronization is possible, therefore a nonlinear system can be driven to a particular state through input from a similar oscillator. Here we expand this concept of control of…
This paper presents a nonlinear approach to measurements a general framework for dealing with variations of environmental conditions. My method may prove promising to extensions beyond classical physics, economics, and other sciences. I…