Related papers: Non Linear System for a Veritable PID Substitute

The Koopman operator framework enables global analysis of nonlinear systems through its inherent linearity. This study aims to clarify spectral properties of the Koopman operators for nonlinear systems with control inputs. To this end, we…

We consider linear elimination of variables in steady state equations of a chemical reaction network. Particular subsets of variables corresponding to sets of so-called reactant-noninteracting species, are introduced. The steady state…

With new advances in machine learning and in particular powerful learning libraries, we illustrate some of the new possibilities they enable in terms of nonlinear system identification. For a large class of hybrid systems, we explain how…

In this paper, we study connections between the classical model-based approach to nonlinear system theory, where systems are represented by equations, and the nonlinear behavioral approach, where systems are defined as sets of trajectories.…

This paper studies controllability of a discrete-time linear dynamical system using nonnegative and sparse inputs. These constraints on the control input arise naturally in many real-life systems where the external influence on the 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…

Consider the problem of covertly controlling a linear system. In this problem, Alice desires to control (stabilize or change the parameters of) a linear system, while keeping an observer, Willie, unable to decide if the system is indeed…

This paper is concerned with robust instability analysis for linear multi-agent dynamical systems with cyclic structure. This relates to interesting and important periodic oscillation phenomena in biology and neuronal science, since the…

This note aims to provide a systematic investigation of direct data-driven control, enriching the existing literature not by adding another isolated result, but rather by offering a unifying, versatile, and broad framework that enables the…

A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical…

Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…

We present a condition for delay-independent stability of a class of nonlinear positive systems. This result applies to systems that are not necessarily monotone and extends recent work on cooperative nonlinear systems.

Computation biology helps to understand all processes in organisms from interaction of molecules to complex functions of whole organs. Therefore, there is a need for mathematical methods and models that deliver logical explanations in a…

A control strategy without any precise mathematical model is derived for linear or nonlinear systems which are assumed to be finite-dimensional. Two convincing numerical simulations are provided.

Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. When the state space is a solvable connected Lie group, controllability of the linear system is assured if the ad-rank condition holds.

For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…

This paper develops a robust safety-critical control method for nonlinear strictfeedback systems with mismatched disturbances. Using a state transformation and a linear time-varying disturbance observer, the system is converted into a form…

Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. For such systems, this paper studies controllability by taking in consideration the eigenvalues of an associated derivation D. When the state…

The problem of linking the structure of a finite linear dynamical system with its dynamics is well understood when the phase space is a vector space over a finite field. The cycle structure of such a system can be described by the…

Linear Hamiltonian systems with time-dependent coefficients are of importance to nonlinear Hamiltonian systems, accelerator physics, plasma physics, and quantum physics. It is shown that the solution map of a linear Hamiltonian system with…