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In natural systems (such as those in natural world) and manmade systems (such as those in
engineering applications), nonlinearity, one of the fundamental characteristics exhibited in simple and
comp...
Robustness Properties of Nonlinear Systems:Absolute Stability of Linear Systems
Robustness Properties Nonlinear Systems Absolute Stability Linear Systems
2015/9/29
Robustness Properties of Nonlinear Systems:Absolute Stability of Linear Systems.
A polynomial-time algorithm for determining quadratic Lyapunov functions for nonlinear systems
Nonlinear systems quadratic lyapunov function and convex programming function
2015/8/12
We consider nonlinear systems dx/dt=f(x(t)) where Df(x(t)) is known to lie in the convex hull of L n times n matrices A_1,ldots,A_L. For such systems, quadratic Lyapunov functions can be determined us...
Empirical Model Reduction of Controlled Nonlinear Systems
Controlled Nonlinear Systems Model Reduction
2015/6/19
In this paper we introduce a new method of model reduction for nonlinear systems with inputs and outputs. The method requires only standard matrix computations, and when applied to linear systems resu...
Empirical Estimators for Stochastically Forced Nonlinear Systems: Observability, Controllability and the Invariant Measure
Empirical Estimators Stochastically Forced Nonlinear Systems Invariant Measure Optimization and Control
2012/4/18
We introduce a data-based approach to estimating key quantities which arise in the study of nonlinear control systems and random nonlinear dynamical systems. Our approach hinges on the observation tha...
Nonexistence of formal first integrals for nonlinear systems under resonance
Non-integrability Resonance First integral Normal form
2011/10/12
In this paper, by using normal form theory we give some criteria of nonexistence of formal first integrals for general nonlinear systems under resonance. As application, we also give a criterion for n...
A modification of the method of characteristics: a new class of multidimensional partially integrable nonlinear systems
modification of the method of characteristics new class of multidimensional partially integrable nonlinear systems
2010/12/28
We represent an algorithm reducing a big class of systems of (M + 1)-dimensional scalar nonlinear partial differential equations (PDEs) to the systems ofM-dimensional first order PDEs. Thus, we integr...
Symmetries, Stability, and Control in Nonlinear Systems and Networks
Nonlinear Systems Networks math
2010/11/8
This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and eq...
One Parameter Scaling Theory for Stationary States of Disordered Nonlinear Systems
Parameter Scaling Stationary States of Disordered Nonlinear Systems
2010/4/6
We show, using detailed numerical analysis and theoretical arguments, that the normalized participation number of the stationary solutions of disordered nonlinear lattices obeys a one-parameter scalin...
One Parameter Scaling Theory for Stationary States of Disordered Nonlinear Systems
One Parameter Scaling Disordered Nonlinear Systems Stationary States
2010/4/6
We show, using detailed numerical analysis and theoretical arguments, that the normalized participation number of the stationary solutions of disordered nonlinear lattices obeys a one-parameter scalin...
A shifted or misaligned feedback loop gives rise to a two-point nonlocality that is the spatial analog of a temporal delay. Important consequences of this nonlocal coupling have been found both in dif...
New Reductions and Nonlinear Systems for 2D Schrodinger Operators
Nonlinear Systems Dubrovin, I.Krichever, S.Novikov 2D Schrodinger Operators
2010/4/1
New Completely Integrable (2+1)-System is studied. It is based on the so-called L-A-B-triples $L_t=[H,L]-fL$ where L is a 2D Schrodinger Operator. This approach was invented by S.Manakov and B.Dubrovi...
Nonlinear systems for highly compressive elasticity simulations
elasticity compressive elasticity
2010/9/15
The standard equations of linear elasticity have served well over many generations to describe small displacements of elastic systems subject to a variety of forces and/or stresses. However, computati...
Prediction of the stochastic behaviour of nonlinear systems by deterministic models as a classical time-passage probabilistic problem
stochastic behaviour nonlinear systems deterministic models time-passage probabilistic problem
2009/11/16
Assuming that the behaviour of a nonlinear stochastic system can be described by a Markovian diffusion approximation and that the evolution equations can be reduced to a system of ordinary differentia...
Adaptive Iterative Learning Control for a Class of Nonlinear Systems with Unknown Control Directions
iterative learning control Unknown Control Directions Nonlinear Systems
2009/9/25
An adaptive iterative learning control(ILC) approach is proposed for a class of uncertain nonlinear systems without prior knowledge about system control directions. The Nussbaum-type gain and the posi...