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

Quadrotor Flight Formation Control via Positive Realness

Optimal Guidance for Rotorcraft Platoon Formation Flying in Wind Fields

In this paper, a guidance law for tracking straight-line segment and a constant-altitude circular orbits are proposed for a fixed wing unmanned aerial vehicle (UAV). Both guidance laws are based on the notion of vector fields, which are used to generate desired commands to the inner-loop attitude controller. Ground track heading error and lateral following error approach zero asymptotically even in an environment with presence of constant wind disturbance. Finally we use the MAV3DSim to validate the develop guidance laws using hardware in the loop simulation.

Vector field guidance law for fixed wing UAV

This paper presents the modeling, the design of control laws, for Euler angles and altitude, and their implementation. The proposed controller is based on the backstepping procedure and uses a state feedback linearizing technique to guarantee tracking of the desired Euler angles and altitude on the ornithopter. The provided controller provides exponential convergence to the desired values. Numerical and experimental applications of the proposed algorithm illustrates the performance of the control technique.

Attitude and altitude control on board of an ornithopter

This paperpresents anadaptive control scheme forfrstordersystemsoftheform= boi+b;u whichmaypossibly benonminimum phase. Thecontrol scheme achieves asymptotical stabilization without anya- priori knowledge ontheplant parameters. Iheadaptive scheme isfree fromsingularities inthesense that theplant estimated model isalways controllable. Thesingularity has beenovercome through a suitable modification ofthe parameters estmates which isbased onstandard least squares covarianc matrix ppertes.

Rogelio Lozano

Papers

Quadrotor Flight Formation Control via Positive Realness

Optimal Guidance for Rotorcraft Platoon Formation Flying in Wind Fields

Vector field guidance law for fixed wing UAV

Attitude and altitude control on board of an ornithopter

Adaptive Stabilization ofNonminimumPhaseFirst Order Continuous-Time Systems