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

Position control of a quad-rotor UAV using vision

This paper deals with developing an automatic controller that solves the attitude stabilization for a Quadrotor unmanned aerial system (UAS). The controller used a simultaneous strategy of estimation and compensation of uncertainties as well as disturbances. The approach consisted of integrating a neuro-fuzzy system that implemented a set of differential neural networks (DNNs) as consequence section of Takagi-Sugeno (T-S) fuzzy inference. The combination of these two strategies applied on a Quadrotor UAS has the main purpose of forcing a hover flight while the tracking desired angular positions are attained. The control method identified the unknown nonlinearities and bounded external disturbances firstly. This information served to compensate the uncertain section of the Quadrotor dynamics. An additional section in the controller design enforces the stabilization of the tracking error with respect to a given reference trajectory. The control design methodology supported on the Lyapunov stability theory and guaranteed ultimate boundedness of the identification and tracking errors. Academic simulation tests confirmed the superior performance of the proposed algorithm based on the combination of DNNs and T-S techniques.

Neuro-fuzzy controller for attitude-tracking stabilization of a multi-rotor unmanned aerial system

Human detection is a very popular field of computer vision. Few works propose a solution for detecting people whatever the camera's viewpoint such as for UAV applications. In this context even state-of-the-art detectors can fail to detect people. We found that the Integral Channel Features detector (ICF) is inoperant in such a context. In this paper, we propose an approach to still benefit from the assets of the ICF while considerably extending the angular robustness during the detection. The main contributions of this work are: 1) a new framework based on the Cluster Boosting Tree and the ICF detector for viewpoint robust human detection, 2) a new training dataset for taking into account the human shape modifications occuring when the pitch angle of the camera changes. We showed that our detector (the PRD) is superior to the ICF for detecting people from complex viewpoints in uncluttered environments and that the computation time of the detector is real-time compatible.

https://hal.archives-ouvertes.fr/hal-01086137/document

Fast and viewpoint robust human detection in uncluttered environments

In this article an adaptive controller is developed in order to estimate the inertia tensor, the mass and the wind parameters (considering wind as a parameter in the input) for the underactuated quad-rotor mini-aircraft. Experimental tests are performed in an educational platform. The proposed control scheme uses the parameter estimation issued from gradient type algorithm. Finally simulations and experimental results are included to illustrate the performance of the parameters identification for the quad-rotor helicopter.

Real-time parameters identification for a quad-rotor mini-aircraft using adaptive control

An approach that uses tools from systems and control theory is presented. Such technique enables the determination of the essential interactions in the autoregulatory process that describes the cell cycle of Xenopus frog eggs. The results make possible an assessment of the effect of each protein on the biochemical network stability. The proposed method is based on bifurcation diagram and linearization near the operating point of interest. A perturbation analysis makes possible the determination of the critical proteins responsible for complex behavior in the system, emphasizing how system theory can play an essential role in the study of these systems.

Rogelio Lozano

Papers

Position control of a quad-rotor UAV using vision

Neuro-fuzzy controller for attitude-tracking stabilization of a multi-rotor unmanned aerial system

Fast and viewpoint robust human detection in uncluttered environments

Real-time parameters identification for a quad-rotor mini-aircraft using adaptive control

Bifurcation analysis of a biochemical network.