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...

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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 chapter is devoted to the design and implementation of a stereo-vision, inertial and altitude sensing system for a quad-rotor. The objective is to enable the vehicle to autonomously perform take-off, relative positioning, navigation and landing when evolving in unstructured, indoors, and GPS-denied environments. A real-time comparison study between a Luenberger observer, a Kalman filter and a complementary filter is also addressed, with the purpose of validating the most effective approach for combining the different sensing technologies.

Combining Stereo Imaging, Inertial and Altitude Sensing Systems for the Quad-Rotor

This paper deals with the references generation for a team of unmanned aerial vehicles tethered to a ground station for inspection applications. In order to deploy the team of vehicles in a suitable location to cover the largest area, each vehicle is commanded to securely navigate in an area of interest while it is tethered to another vehicle or to a ground station. To generate the corresponding reference for each vehicle, we used a model predictive controller, which optimizes the desired trajectory based on the mission-defined constraints. To validate the effectiveness of the proposed strategy, we conducted a simulation and experimental tests with a team of consumer unmanned aerial vehicles tethered to a ground station.

/pdf/reference-generator-for-a-system-of-multiple-tethered-25wkrctf.pdf

Reference Generator for a System of Multiple Tethered Unmanned Aerial Vehicles

In this paper, the modeling and robust control design of a vertical flight attitude control for a mini tail-sitter with variable pitch propeller is discussed. Tail-sitters Vertical Take-off and Landing - Unmanned Aerial Vehicles (VTOL-UAVs) have operational flexibility of typical helicopters while having the cruise performance of fixed wing airplanes. The configuration proposed in this work is highly unstable in its natural flight state in vertical mode. A simplified dynamic model is presented and a robust control design to stabilize the decoupled attitude systems in presence of uncertainty and time-delay is developed. The results are supported by simulation tests.

Rogelio Lozano

Papers

Combining Stereo Imaging, Inertial and Altitude Sensing Systems for the Quad-Rotor

Reference Generator for a System of Multiple Tethered Unmanned Aerial Vehicles

Robust control design for a class of Unmanned Aerial Vehicle with parametric uncertainty

Local Adaptive Stabilization of a First Order Nonlinear System Without Lipschitz Assumptions