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

Building inspection searching for superficial defects, such as cracks, is a vital task because such damages cause economic losses or put at risk the integrity of people For this reason, different ways to reduce the costs and risks through the use of robotic systems that allow make inspections have been studied Among these robotic systems, we have the unmanned aerial vehicles (UAV) that allow reaching difficult access places permitting better inspection In this work, we propose using convolutional neuronal networks for crack recognition from images captured by an UAV To carry out the training task of the network, a database of cracks in walls was built from images collected from the Internet The training of the network prompted encouraging results with a 95% accuracy over the training set Experimental results of crack recognition in images were carried out validating the application of the proposal

Towards automatic inspection: crack recognition based on Quadrotor UAV-taken images

We discuss the nonlinear control of a novel biped robot with three-degrees-of-freedom and two control inputs, whose dynamics are linear apart from the gravitational torque and the impact equations. We show that the equations of motion are locally feedback linearizable by nonlinear change of coordinates and nonlinear feedback in a region that includes all walking gaits of interest. We combine the feedback linearization control with control of the resulting linear system and the nonlinear impact equations to generate a stable walking gait.

Rogelio Lozano

Papers

Towards automatic inspection: crack recognition based on Quadrotor UAV-taken images

An almost linear biped

2-Sliding Mode Trajectory Tracking Control and EKF Estimation for Quadrotors

Modeling and Control of a Convertible Mini-UAV

Model reference adaptive control with unknown high frequency gain sign