In this paper we deal with the control of chaotic systems. Knowing that a chaotic attractor contains a myriad of unstable periodic orbits (UPO's), the aim of our work is to stabilize some of the UPO's embedded in the chaotic attractor and which have interesting characteristics. First, using the input-tostate linearization method in conjunction with a timedelayed state feedback, we design a control signal that can achieve stabilization. Next, an adaptive timedelayed state feedback is proposed which shows at once efficiency and simplicity and circumvents the construction complexity of the first controller. Finally, we propose a reduced order sliding mode observer to estimate the necessary states for the design of an adaptive time delayed state feedback controller. This last controller has one main advantage, it in fact achieves UPO stabilization without using the system model. The efficacy of the proposed methods is illustrated by numerical simulations onto Chua's system.A. Fourati · M. Feki ( ) · N. Derbel

Structural identifiability is a fundamental prerequisite For parametric model identification. It concerns uniqueness of the parametric structure given a dynamical model and a set of inputloutput experimental dates. Proving structural identifiability propriety for non linear systems is considered until now a very difficult problem. Many approaches have been proposed in the litcrature but there isn't a generic method suitable for any non linear case. The main concern of this paper is to present an overview of different approaches used to test siruciural identifiability for non linear systems. Important aspects and difficulties of identifiability analysis will be reviewed and illustrated by an example of an actived sludge process characterized by rational polynomial non linearities and specified initial conditions.

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