A geometrical characterization of a class of 00-flat affine dynamical systems

International audienceThis paper gives a description of a class of $0$-flat dynamical systems. This class is characterized by the involutivity of a distribution associated naturally to multi-output affine dynamical systems and the Lie bracket of some control vector fields fulfilling some conditions. We will also show that these conditions are a generalization of the well-known result on $0$-flatness of codimension $1$ affine systems

Discussion about Sliding Mode Algorithms, Zeno Phenomena and Observability

Lecture Notes in Control and Information Sciences, 2012, Volume 412/2012, 199-219, DOI: 10.1007/978-3-642-22164-4_7.This chapter is devoted to a discussion about the relations between first and high order sliding mode algorithms and both types of Zeno (Chattering and Genuinely) behaviors of switched dynamical systems. Firstly, the Henstock-Kurzweil integral is recalled in order to set up the problem of switched systems with Zeno phenomena, which enables to include Filippov solution and take into account some singularities. Then, observer designs based on the well-known super twisting algorithm are proposed. For this kind of problems, the importance of finite time convergence of the observation error is studied, and some simulations are given to highlight the discussion. Lastly, the two tanks example is given in order to point out the differences between both Zeno phenomena types, to show that there is life after Zeno and that a higher order sliding mode observer can be efficient before, during and after both Zeno phenomena types

A new reduced-order observer normal form for nonlinear discrete time systems

International audienceThis paper presents a new observability normal form for discrete-time nonlinear systems. This form enables us to design a reduced-order observer. Necessary and sufficient geometrical conditions for the existence of a coordinate change to transform a discrete-time nonlinear system into such normal form are given. An illustrative example is given to show the effectiveness of our approach

Observer normal forms for a class of Predator-Prey models

There is a wide body of scientific literature on the well-known Predator-Prey ecological models. However, just a few number of published articles deal with the problem of observer design for these dynamical systems. The aim of this paper is to apply the nonlinear observer normal forms to address this problem. We first introduce the notion of nonlinear observer normal forms that allows one to design robust nonlinear observers for a class of Predator-Prey systems, whose state variables are not all measurable. Then, we apply these normal forms to several different Predator-Prey systems. Numerical examples are also provided to show the efficiency of the proposed method, where we globally estimate the unmeasurable populations of a Predator-Prey system using a measured population of one species (prey or predator)

Sliding mode observers and observability singularity in chaotic synchronization

We present a new secured data transmission based on a chaotic synchronization and observability singularity. For this, we adopt an approach based on an inclusion of the message in the system structure and we use a sliding mode observer for system with unknown input in order to recover the information. We end the paper with an example of chaotic system with an observability bifurcation. Moreover, this example highlights some benefits of the so-called step-by-step sliding mode observer