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

Nowadays pedestrian detectors are fast, scale-robust and quite efficient. Embedded within a UAV such a detector would open new possibilities. In this paper the very well known HOG detector is adapted for UAV use and a new kind of training dataset is proposed in order to increase the detector's angular robustness. A more appropriate set of detection windows, together with a new detection pipeline, is proposed in order to reduce the search space and consequently reduce the computation time. Tests conducted using the improved detector show significantly better results on aerial images.

/pdf/human-detection-in-uncluttered-environments-from-ground-to-260ydgbnvu.pdf

Human detection in uncluttered environments: From ground to UAV view

The problem of vision-based road following using a quad-rotor is addressed The objective consists of estimating and tracking a road without a priori knowledge of such path For this purpose, two operational regions are defined: one for the case when the road is detected, and the other one for when it is not A switching between imaging and inertial sensors measurements allows estimating the required vehicle's parameters in both regions Also, for dealing with both aforementioned cases, a switching control strategy which stabilizes the vehicle's lateral position is proposed The performance of the proposed switching methodologies is tested in real time experiments

/pdf/quad-rotor-switching-control-an-application-for-the-task-of-4duvrk3728.pdf

Quad-rotor switching control: An application for the task of path following

http://users.cecs.anu.edu.au/~Robert.Mahony/Mahony_Robert/2000_LozDimMah-J15.pdf

Brief Identification of linear time-varying systems using a modified least-squares algorithm

Presents an adaptive control scheme for first order systems of the form y/spl dot/+a*y=b/sub 0/*u/spl dot/+b/sub 1/*u which may possibly be a nonminimum phase. The control scheme achieves asymptotical stabilization without any a priori knowledge on the plant parameters. The adaptive scheme is free from singularities in the sense that the plant estimated model is always controllable. The singularity has been overcome through a suitable modification of the parameter estimates, which is based on standard least squares covariance matrix properties, and the use of a hysteresis switching function. >

Adaptive stabilization of nonminimum phase first-order continuous-time systems

The authors present an adaptive control scheme for nonlinear systems of the form x=c/sup *T/ f(x)+b/sup */u, where f(x) is Lipschitz, c/sup */ is a constant vector, and b/sup */ is a constant scalar. The control scheme achieves asymptotical model matching without a priori knowledge of the sign of the b/sup */ gain. The adaptive scheme is free from singularities in the sense that the estimate of b/sup */, entering in the denominator of the control law, is bounded away from zero. The singularity has been overcome through a suitable modification of the parameters estimates which is based on standard least squares covariance matrix properties. >

/pdf/adaptive-control-of-a-simple-nonlinear-system-without-a-33ovyex38p.pdf

Rogelio Lozano

Papers

Human detection in uncluttered environments: From ground to UAV view

Quad-rotor switching control: An application for the task of path following

Brief Identification of linear time-varying systems using a modified least-squares algorithm

Adaptive stabilization of nonminimum phase first-order continuous-time systems

Adaptive control of a simple nonlinear system without a-priori information on the plant parameters