Iterative approximation of limit cycles for a class of Abel equations

This article considers the analytical approximation of limit cycles that may appear in Abel equations written in the normal form. The procedure uses an iterative approach that takes advantage of the contraction mapping theorem. Thus, the obtained sequence exhibits uniform convergence to the target periodic solution. The effectiveness of the technique is illustrated through the approximation of an unstable limit cycle that appears in an Abel equation arising in a tracking control problem that affects an elementary, second-order bilinear power converter.     

Reconstructeurs d'état

In contrast to Kalman filters and asymptotic observers, the state reconstructors do not need the integration of differential equations. They eliminate structured perturbations and are robust with respect to noises without any precise knowledge of their statistical properties. The techniques used are, primarily, of algebraic nature. To cite this article: M. Fliess, H. Sira-Ram??rez, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Compression différentielle de transitoires bruités

The analysis and compression of noisy transient signals are handled via methods stemming from elementary differential algebra, noncommutative algebra and operational calculus. The efficiency of our approach is illustrated by an academic example and a more concrete case-study which is a musical signal. To cite this article: M. Fliess et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

A linear differential flatness approach to controlling the Furuta pendulum

^** Email: caguilar{at}cic.ipn^*** Email: hsira{at}mail.cinvestav.mx The aim of this work is to motivate the use of linear flatness,or controllability, to design a feedback control law for therather challenging mechanism known as the ‘Furuta pendulum’.This is achieved by introducing three feedback controller designoptions for the stabilization and rest-to-rest trajectory trackingtasks: a direct pole placement approach, a hierarchical high-gainapproach and a generalized proportional integral approach synthesizedon the basis of measured inputs and outputs.