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Robust Feedback Control Design for a Nonlinear Wastewater Treatment Model

M. Serhani, N. Raissi, P. Cartigny (2009)

Mathematical Modelling of Natural Phenomena

In this work we deal with the design of the robust feedback control of wastewater treatment system, namely the activated sludge process. This problem is formulated by a nonlinear ordinary differential system. On one hand, we develop a robust analysis when the specific growth function of the bacterium μ is not well known. On the other hand, when also the substrate concentration in the feed stream sin is unknown, we provide an observer of system and propose a design of robust feedback control in...

Robust transitivity in hamiltonian dynamics

Meysam Nassiri, Enrique R. Pujals (2012)

Annales scientifiques de l'École Normale Supérieure

A goal of this work is to study the dynamics in the complement of KAM tori with focus on non-local robust transitivity. We introduce C r open sets ( r = 1 , 2 , ⋯ , ∞ ) of symplectic diffeomorphisms and Hamiltonian systems, exhibitinglargerobustly transitive sets. We show that the C ∞ closure of such open sets contains a variety of systems, including so-calleda priori unstable integrable systems. In addition, the existence of ergodic measures with large support is obtained for all those systems. A main ingredient of...

Rosen fractions and Veech groups, an overly brief introduction

Thomas A. Schmidt (2009)

Actes des rencontres du CIRM

We give a very brief, but gentle, sketch of an introduction both to the Rosen continued fractions and to a geometric setting to which they are related, given in terms of Veech groups. We have kept the informal approach of the talk at the Numerations conference, aimed at an audience assumed to have heard of neither of the topics of the title.The Rosen continued fractions are a family of continued fraction algorithms, each gives expansions of real numbers in terms of elements of a corresponding algebraic...

Rotation sets for graph maps of degree 1

Lluís Alsedà, Sylvie Ruette (2008)

Annales de l’institut Fourier

For a continuous map on a topological graph containing a loop S it is possible to define the degree (with respect to the loop S ) and, for a map of degree 1 , rotation numbers. We study the rotation set of these maps and the periods of periodic points having a given rotation number. We show that, if the graph has a single loop S then the set of rotation numbers of points in S has some properties similar to the rotation set of a circle map; in particular it is a compact interval and for every rational...

Rotation sets for subshifts of finite type

Krystyna Ziemian (1995)

Fundamenta Mathematicae

For a dynamical system (X,f) and a function φ : X → ℝ N the rotation set is defined. The case when (X,f) is a transitive subshift of finite type and φ depends on the cylinders of length 2 is studied. Then the rotation set is a convex polyhedron. The rotation vectors of periodic points are dense in the rotation set. Every interior point of the rotation set is a rotation vector of an ergodic measure.

Ruelle operator with nonexpansive IFS

Ka-Sing Lau, Yuan-Ling Ye (2001)

Studia Mathematica

The Ruelle operator and the associated Perron-Frobenius property have been extensively studied in dynamical systems. Recently the theory has been adapted to iterated function systems (IFS) ( X , w j j = 1 m , p j j = 1 m ) , where the w j ’s are contractive self-maps on a compact subset X ⊆ ℝ d and the p j ’s are positive Dini functions on X [FL]. In this paper we consider Ruelle operators defined by weakly contractive IFS and nonexpansive IFS. It is known that in such cases, positive bounded eigenfunctions may not exist in general. Our theorems...

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