Global tracking for an underactuated ships with bounded feedback controllers

In this paper, we present a global state feedback tracking controller for underactuated surface marine vessels. This controller is based on saturated control inputs and, under an assumption on the reference trajectory, the closed-loop system is globally asymptotically stable (GAS). It has been designed using a 3 Degree of Freedom benchmark vessel model used in marine engineering. The main feature of our controller is the boundedness of the control inputs, which is an essential consideration in real life. In absence of velocity measurements, the controller works and remains stable with observers and can be used as an output feedback controller. Simulation results demonstrate the effectiveness of this method

A Lyapunov approach to Robust and Adaptive Higher Order Sliding Mode

In this paper, we present Lyapunov-based robust and adaptive Higher Order Sliding Mode (HOSM) controllers for nonlinear SISO systems with bounded uncertainty. The proposed controllers can be designed for any arbitrary sliding mode order. The uncertainty bounds are known in the robust control problem whereas they are partially known in the adaptive control problem. Both these problems are formulated as the finite time stabilization of a chain of integrators with bounded uncertainty. The controllers are developed from a class of nonlinear controllers which guarantee finite time stabilization of pure integrator chains. The robust controller establishes ideal HOSM i.e. the sliding variable and its r−1 time derivatives converge exactly to the origin in finite time. The adaptive controller establishes real HOSM, which means that the sliding variable and its r - 1 time derivatives converge to a neighborhood of the origin. Saturation functions are used for gain adaptation, which do not let the states exit the neighborhood after convergence. The effectiveness of these controllers is illustrated through simulations

LpL_p-stabilization of integrator chains subject to input saturation using Lyapunov-based homogeneous design

Consider the $n$-th integrator $\dot x=J_nx+\sigma(u)e_n$, where $x\in\mathbb{R}^n$, $u\in \mathbb{R}$, $J_n$ is the $n$-th Jordan block and $e_n=(0\ \cdots 0\ 1)^T\in\mathbb{R}^n$. We provide easily implementable state feedback laws $u=k(x)$ which not only render the closed-loop system globally asymptotically stable but also are finite-gain $L_p$-stabilizing with arbitrarily small gain. These $L_p$-stabilizing state feedbacks are built from homogeneous feedbacks appearing in finite-time stabilization of linear systems. We also provide additional $L_\infty$-stabilization results for the case of both internal and external disturbances of the $n$-th integrator, namely for the perturbed system $\dot x=J_nx+e_n\sigma (k(x)+d)+D$ where $d\in\mathbb{R}$ and $D\in\mathbb{R}^n$

Vertebral cryptococcosis in an immunocompetent patient - a case report

We report an unusual case of 70 years old, immunocompetent woman who was diagnosed with vertebral cryptococcosis. The diagnosis was made on the basis of radiological and histological findings. The outcome was favorable under antifungal treatment

Méningite récurrente révélant une maladie de Behçet: à propos de deux cas

Les étiologies des méningites sont surtout infectieuses. Les causes non infectieuses, sont souvent de  diagnostic difficile et incertain, tel est le cas de la maladie de Behçet. Nous rapportons deux observations de patients ayant présenté des épisodes récurrents de méningite. Dans un premier temps, la suspicion d’une étiologie infectieuse a conduit à introduire un traitement anti-infectieux probabiliste. La découverte à posteriori d’une aphtose bipolaire a permis de poser le diagnostic de maladie de Behçet. Une corticothérapie s’est révélée efficace. La maladie de Behçet doit toujours faire partie des diagnostics différentiels des méningites récurrentes.Key words: Méningite récurrente, maladie de Behçet, neuro-Behçe