Characterization of Safety and Conditional Invariance for Nonlinear Systems

2019 ◽  
Author(s):  
Mohamed Maghenem ◽  
Ricardo G. Sanfelice
Keyword(s):  
Nonlinear Systems ◽  
Conditional Invariance

Strict convexity, strong ellipticity, and regularity in the calculus of variations

1980 ◽  
Vol 87 (3) ◽  
pp. 501-513 ◽  
Author(s):  
J. M. Ball
Keyword(s):  
Nonlinear Systems ◽  
Calculus Of Variations ◽  
Weak Solutions ◽  
Convex Functions ◽  
Strict Convexity ◽  
Mathematical Tool ◽  
Strong Ellipticity ◽  
Regularity Of Weak Solutions ◽  
Nonlinear Elastostatics

In this paper we investigate the connection between strong ellipticity and the regularity of weak solutions to the equations of nonlinear elastostatics and other nonlinear systems arising from the calculus of variations. The main mathematical tool is a new characterization of continuously differentiable strictly convex functions. We first describe this characterization, and then explain how it can be applied to the calculus of variations and to elastostatics.

scholarly journals DYNAMICAL DISORDER AND SELF-CORRELATION IN THE CHARACTERIZATION OF NONLINEAR SYSTEMS: APPLICATION TO DETERMINISTIC CHAOS

2011 ◽  
Vol 21 (03) ◽  
pp. 963-983 ◽  
Author(s):  
JUAN ANTONIO HERNÁNDEZ ◽  
ROSA MARÍA BENITO ◽  
JUAN CARLOS LOSADA
Keyword(s):  
Nonlinear Systems ◽  
Scalar Product ◽  
Chaotic Systems ◽  
Deterministic Chaos ◽  
The Self ◽  
One Dimension ◽  
Two Dimensional ◽  
Dynamical Order ◽  
Dynamical Disorder

A new methodology to characterize nonlinear systems is described. It is based on the measurement over the time series of two quantities: the "Dynamical order" and the "Self-correlation". The averaged "Scalar" and "Perpendicular" products are introduced to measure these quantities. While this approach can be applied to general nonlinear systems, the aim of this work is to focus on the characterization and modeling of chaotic systems. In order to illustrate the method, applications to a two-dimensional chaotic system and the modeling of real telephony traffic series are presented. Three important aspects are discussed: the use of the averaged "Scalar" product as supplement of the "Lyapunov exponent", the use of the averaged "Perpendicular" product as a refinement of the "Mutual information" and the reduction of m-dimensional systems to the study of only one dimension. This new conceptual framework introduces a perspective to characterize real and theoretical processes with a unifying method, irrespective of the system classification.

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