There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Time-delay systems: an overview of some recent advances and open problems

Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree of the constraint has to be 1 and a dangerous chattering effect is possible. Higher-order sliding modes preserve or generalize the main properties of the standard sliding mode and remove the above restrictions. r-Sliding mode realization provides for up to the rth order of sliding precision with respect to the sampling interval compared with the first order of the standard sliding mode. Such controllers require higher-order real-time derivatives of the outputs to be available. The lacking information is achieved by means of proposed arbitrary-order robust exact differentiators with finite-time convergence. These differentiators feature optimal asymptot...

/pdf/higher-order-sliding-modes-differentiation-and-output-438zdzb0ld.pdf

Higher-order sliding modes, differentiation and output-feedback control

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

This work focuses on the nonlinear control of helicopters Our global interest is a general model (7-DOF) to be used on the autonomous forward-flight of helicopters However, in this paper we present a reduced-order model (3-DOF) representing a scale model helicopter mounted on an experimental platform In this system the vertical flight of the helicopter can be studied Although simplified, this 3-DOF Lagrangian model presents quite interesting control challenges due to nonlinearities, aerodynamical forces and underactuation Due to the very particular dynamical and control properties of the 3-DOF model we propose a specific nonlinear controller using passivity properties to control the rotational part of the system An I/O linearizing controller is used for the helicopter altitude control Numerical simulations are presented to illustrate the performance of these controllers

Nonlinear control of helicopters

Nowadays, control problems of underactuated vehicles motivate the development of new non-linear control design methodologies. Such systems are vehicles with fewer independent control inputs than degrees of freedom to be controlled.

The hovercraft model

Modelisation et stabilisation avec des entrees bornees d’un petit helicoptere possedant deux rotors pivotants Farid Kendoul∗ , Isabelle Fantoni, Rogelio Lozano Heudiasyc, UMR CNRS 6599, UTC, BP 20529 60205 Compiegne, France email :{fkendoul, ifantoni, rlozano}@hds.utc.fr RESUME Dans ce papier, nous avons presente une nouvelle confi- guration pour un drone miniature autonome. Ce der- nier utilise un mecanisme de controle original qui com- porte deux rotors montes lateralement. La direction de la poussee totale peut etre obtenue en forcant les rotors a pivoter lateralement et longitudinalement. L’etude de ce mecanisme montre que les couples necessaires pour la commande peuvent etre obtenus en exploitant la nature gyroscopique des rotors pivotants. Cette confi- guration a ete aussi validee sur deux prototypes que nous avons construits. Apres avoir decrit la modeli- sation de la dynamique de l’helicoptere birotor, nous avons propose une loi de commande basee sur des sa- turations imbriquees qui a permis de prendre en compte les contraintes reelles sur les entrees de commande. Les resultats de simulation ont montre les bonnes perfor- mances d

Modélisation et stabilisation avec des entrées bornées d’un petit hélicoptère possédant deux rotors pivotants

The present paper addresses the transition stage of a Gun-Launched Micro Air Vehicle (GLMAV) whose main goal is to rapidly position a rotorcraft MAV over a high-risk scene (Prison riots, blind zones: e.g. over-the-hill, etc.). The development of this robotic platform is part of an overall ongoing project (GLMAV) headed by the St. Louis French- German Research Institute (ISL). The vehicle is launched at a distance of 500 m and a height of 100 m, where the GLMAV will collect and transmit visual information from the scene. Issues raising from the use of the gun-based launching technique are discussed in detail. A control strategy is proposed to overcome such problems and to stabilize the GLMAV. High- fidelity simulations, covering ballistic and transition phases, validate the control policy adopted to face the MAV gun- launching problem.

The Transition Phase of a Gun-Launched Micro Air Vehicle

Indirect adaptive control is a widely applicable adaptive control strategy. In real-time, it combines plant model parameter estimation in closed loop with the redesign of the controller. Adaptive pole placement and its robustified version, together with adaptive generalized predictive control constitute the core of the chapter. Adaptive linear quadratic control is also presented. Application of various strategies for the indirect adaptive control of a flexible transmission illustrates the methodology presented in this chapter.

Rogelio Lozano

Papers

Nonlinear control of helicopters

The hovercraft model

Modélisation et stabilisation avec des entrées bornées d’un petit hélicoptère possédant deux rotors pivotants

The Transition Phase of a Gun-Launched Micro Air Vehicle

Indirect Adaptive Control