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On the anti–synchronization detection for the generalized Lorenz system and its applications to secure encryption

Volodymyr Lynnyk, Sergej Čelikovský (2010)

Kybernetika

In this paper, a modified version of the Chaos Shift Keying (CSK) scheme for secure encryption and decryption of data will be discussed. The classical CSK method determines the correct value of binary signal through checking which initially unsynchronized system is getting synchronized. On the contrary, the new anti-synchronization CSK (ACSK) scheme determines the wrong value of binary signal through checking which already synchronized system is loosing synchronization. The ACSK scheme is implemented...

On the best observation of wave and Schrödinger equations in quantum ergodic billiards

Yannick Privat, Emmanuel Trélat, Enrique Zuazua (2012)

Journées Équations aux dérivées partielles

This paper is a proceedings version of the ongoing work [20], and has been the object of the talk of the second author at Journées EDP in 2012.In this work we investigate optimal observability properties for wave and Schrödinger equations considered in a bounded open set Ω ⊂ ℝ n , with Dirichlet boundary conditions. The observation is done on a subset ω of Lebesgue measure | ω | = L | Ω | , where L ∈ ( 0 , 1 ) is fixed. We denote by 𝒰 L the class of all possible such subsets. Let T > 0 . We consider first the benchmark problem of maximizing...

On the Charney Conjecture of Data Assimilation Employing Temperature Measurements Alone: The Paradigm of 3D Planetary Geostrophic Model

Aseel Farhat, Evelyn Lunasin, Edriss S. Titi (2016)

Mathematics of Climate and Weather Forecasting

Analyzing the validity and success of a data assimilation algorithmwhen some state variable observations are not available is an important problem in meteorology and engineering. We present an improved data assimilation algorithm for recovering the exact full reference solution (i.e. the velocity and temperature) of the 3D Planetary Geostrophic model, at an exponential rate in time, by employing coarse spatial mesh observations of the temperature alone. This provides, in the case of this paradigm,...

On the circle criterion for boundary control systems in factor form : Lyapunov stability and Lur’e equations

Piotr Grabowski, Frank M. Callier (2006)

ESAIM: Control, Optimisation and Calculus of Variations

A Lur’e feedback control system consisting of a linear, infinite-dimensional system of boundary control in factor form and a nonlinear static sector type controller is considered. A criterion of absolute strong asymptotic stability of the null equilibrium is obtained using a quadratic form Lyapunov functional. The construction of such a functional is reduced to solving a Lur’e system of equations. A sufficient strict circle criterion of solvability of the latter is found, which is based on results...

On the circle criterion for boundary control systems in factor form: Lyapunov stability and Lur'e equations

Piotr Grabowski, Frank M. Callier (2005)

ESAIM: Control, Optimisation and Calculus of Variations

A Lur'e feedback control system consisting of a linear, infinite-dimensional system of boundary control in factor form and a nonlinear static sector type controller is considered. A criterion of absolute strong asymptotic stability of the null equilibrium is obtained using a quadratic form Lyapunov functional. The construction of such a functional is reduced to solving a Lur'e system of equations. A sufficient strict circle criterion of solvability of the latter is found, which is based on...

On the constrained controllability of dynamical systems with multiple delays in the state

Beata Sikora (2003)

International Journal of Applied Mathematics and Computer Science

Linear stationary dynamical systems with multiple constant delays in the state are studied. Their relative and approximate controllability properties with constrained controls are discussed. Definitions of various types of controllability with constrained controls for systems with delays in the state are introduced. Some theorems concerning the relative and the approximate relative controllability with constrained controls for dynamical systems with delays in the state are established. Various types...

On the controllability and stabilization of the linearized Benjamin-Ono equation

Felipe Linares, Jaime H. Ortega (2005)

ESAIM: Control, Optimisation and Calculus of Variations

In this work we are interested in the study of controllability and stabilization of the linearized Benjamin-Ono equation with periodic boundary conditions, which is a generic model for the study of weakly nonlinear waves with nonlocal dispersion. It is well known that the Benjamin-Ono equation has infinite number of conserved quantities, thus we consider only controls acting in the equation such that the volume of the solution is conserved. We study also the stabilization with a feedback law which...

On the controllability and stabilization of the linearized Benjamin-Ono equation

Felipe Linares, Jaime H. Ortega (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this work we are interested in the study of controllability and stabilization of the linearized Benjamin-Ono equation with periodic boundary conditions, which is a generic model for the study of weakly nonlinear waves with nonlocal dispersion. It is well known that the Benjamin-Ono equation has infinite number of conserved quantities, thus we consider only controls acting in the equation such that the volume of the solution is conserved. We study also the stabilization with a feedback law...

On the controllability of fractional dynamical systems

Krishnan Balachandran, Jayakumar Kokila (2012)

International Journal of Applied Mathematics and Computer Science

This paper is concerned with the controllability of linear and nonlinear fractional dynamical systems in finite dimensional spaces. Sufficient conditions for controllability are obtained using Schauder's fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. Examples are given to illustrate the effectiveness of the theory.

On the controllability of the 1-D isentropic Euler equation

Olivier Glass (2007)

Journal of the European Mathematical Society

We study the controllability problem for the one-dimensional Euler isentropic system, both in Eulerian and Lagrangian coordinates, by means of boundary controls, in the context of weak entropy solutions. We give a sufficient condition on the initial and final states under which the first one can be steered to the latter.

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