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

An adaptive control scheme for manipulators with redundant degrees of freedom is presented. The control purpose is to achieve a desired interaction force between the end-effector and the environment as well as to regulate the robot tip position in the Cartesian space. This control approach does not require measurement of the joint acceleration or the force derivative. >

Adaptive hybrid force-position control for redundant manipulators

We introduce an original configuration of a multi rotor helicopter composed of eight rotors. Four rotors, also called main rotors, are used to stabilize the attitude of the helicopter, while the four extra rotors (lateral rotors) are used to perform the lateral movements of the unmanned aerial vehicle (UAV). The main characteristic of this configuration is that the attitude and translation dynamics are decoupled. The dynamic model is obtained using the well known Euler---Lagrange approach. To validate the model, we performed real-time experiments using a simple nonlinear control law using optical flow and image processing.

Modeling and Real-Time Stabilization of an Aircraft Having Eight Rotors

This chapter presents the modeling of a quad-rotor UAV A general overview of the quad-rotor helicopter and its operation principle is given Next, the quad-rotor modeling is addressed using two different approaches: Euler–Lagrange and Newton–Euler How to derive Lagrange’s equations from Newton’s equations is also shown Finally, the author presents also the Newton–Euler modeling for an “X-Flyer” quad-rotor configuration

Modeling the Quad-Rotor Mini-Rotorcraft

In this paper we consider a special class of integral delay systems arising in several stability problems of time-delay systems. For these integral systems we derive stability and robust stability conditions in terms of Lyapunov–Krasovskii functionals. More explicitly, after providing the stability conditions we compute quadratic functionals and apply them to derive exponential estimates for solutions, and robust stability conditions for perturbed integral delay systems. Copyright © 2008 John Wiley & Sons, Ltd.

Stability conditions for integral delay systems

This article presents a comparison of three control techniques: nested saturations, backstepping, and sliding modes. The control objective consists of obtaining the best control strategy to stabilize the position of a quad-rotor unmanned aerial vehicle (UAV) when using visual feedback. We propose a vision-based method to measure translational speed as well as the UAV 3D position in a local frame. The three selected controllers were implemented and tested in real-time experiments. The obtained results demonstrate the performance of such methodologies applied to the quad-rotor system.

https://hal.archives-ouvertes.fr/hal-00776033/document

Rogelio Lozano

Papers

Adaptive hybrid force-position control for redundant manipulators

Modeling and Real-Time Stabilization of an Aircraft Having Eight Rotors

Modeling the Quad-Rotor Mini-Rotorcraft

Stability conditions for integral delay systems

Hovering Quad-Rotor Control: A Comparison of Nonlinear Controllers using Visual Feedback