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

http://wks.gii.upv.es/sidireli/files/TDS_XG-643_FINAL.pdf

Robustness of a discrete-time predictor-based controller for time-varying measurement delay

A simplified model of the dynamics of an autonomous model helicopter valid for manoeuvres close to hover is considered The control task is to track a given path in the position co-ordinates as accurately as possible This is made difficult since the model contains weakly non-minimum phase zero dynamics which cannot be stably inverted By placing constraints on the physical weight distribution associated with the necessary sensor and computer components that must be carried by the autonomous unit a new representation the dynamics of the system in block pure feedback form is derived The exact tracking problem is solved using input/output linearization techniques

Almost) exact path tracking control for an autonomous helicopter in hover manoeuvres

In this paper we address the problem of real-time optimal trajectory generation of a micro Air Vehicle (MAV) in unknown and low-sunlight environments. The MAV is required to navigate from an initial and outdoor position to a final position inside of a building. In order to achieve this goal, the MAV must estimate a window of the building. For this purpose, we develop a safe path planning method using the information provided by the GPS and a consumer depth camera. With the aim of developing a safe path planning with obstacle avoidance capabilities, a model predictive control approach is developed, which uses the environment information acquired by the navigation system. The results are tested on simulations and some preliminary experimental results are given. Our system's ability to identify and estimate a window model and the relative position w.r.t. the window is demonstrated through video sequences collected from the experimental platform.

/pdf/a-vision-and-gps-based-real-time-trajectory-planning-for-a-4yvwukic89.pdf

A Vision and GPS-Based Real-Time Trajectory Planning for a MAV in Unknown and Low-Sunlight Environments

We present a dynamical model of an original trirotor helicopter obtained using the Euler-Lagrange approach. The obtained nonlinear model is then used for designing a nonlinear controller based on nested saturations. The controller performance is shown in real-time experiments.

Stabilization and nonlinear control for a novel trirotor mini-aircraft

A helicopter offers the capability of hover, slow forward displacement, vertical take-off and landing while a conventional airplane has the performance of fast forward movement, long reach and superior endurance. The aim of this paper is to present the modelling and control of a tilt tri-rotor UAV's configuration that combines the advantages of both rotary wing and fixed wing vehicle.

/pdf/modeling-and-control-of-a-tilt-tri-rotor-airplane-285ahkubzs.pdf

Rogelio Lozano

Papers

Robustness of a discrete-time predictor-based controller for time-varying measurement delay

Almost) exact path tracking control for an autonomous helicopter in hover manoeuvres

A Vision and GPS-Based Real-Time Trajectory Planning for a MAV in Unknown and Low-Sunlight Environments

Stabilization and nonlinear control for a novel trirotor mini-aircraft

Modeling and control of a tilt tri-rotor airplane