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

In recent years, solar energy has been used as an energy source for many different applications. Currently in the area of Unmanned Aerial Vehicles (UAVs), there are research studies that incorporate this renewable energy technology to increase the vehicle’s autonomy. This technique also needs particular construction techniques and electronic boards, designed to reduce weight and increase the efficiency of all solar systems on board the UAV. As is well known, the amount of generated solar energy could be increased throughout a day a sun tracking technique is added. The present paper proves that the roll angle of a fixed wing UAV can be used to track the sun to increase the energy generated by the solar panels placed on the wing. In that case, the plane’s attitude must be compensated with the yaw angle control to be able to perform a photogrammetric mission. This will be achieved using a control strategy based on the super-twisting technique that ensures convergence in finite time even in the presence of bounded perturbations. The design of the control laws as well as the numerical simulation and real flight results are shown to validate the use of the sun tracking system.

https://www.mdpi.com/2504-446X/3/2/51/pdf

Sun Tracking Technique Applied to a Solar Unmanned Aerial Vehicle

Robust adaptive control of a class of nonlinear first order systems

The exoskeletons are bio-mechanisms used for amplification of strength, load heavy objects, increase speed and human resistance. for this reason the exoskeletons have many medical and military applications. The present paper concerns about construction and control of exoskeleton assisted by SEA (Series Elastic Actuators) having two degrees of freedom (knee and ankle). This exoskeleton offers a reduction in effort required by the user to reach and keep the stand up position as well as to performs some exercises like flexing the leg, etc.

Modeling and control of a lower limb exoskeleton with two degrees of freedom

Summary

This paper proposes a control scheme for the problem of stabilizing partly unknown multiple-input multiple-output linear time-varying retarded systems. The control scheme is composed by a singularly perturbed controller and a reference model. We assume the knowledge of a number of structural characteristics of the system as the boundedness and the knowledge of the bounds for the unknown parameters (and their derivatives) that define the system matrices, as well as the structure of these matrices. The results presented here are a generalization of previous results on linear time-varying Single-Input Single-Output (SISO) and multiple-input multiple-output systems without delays and linear time-varying retarded SISO systems. The closed-loop system is a linear singularly perturbed retarded system with uniform asymptotic stability behavior. The uniform asymptotic stability of the singularly perturbed retarded system is guaranteed. We show how to design a control law such that the system dynamics for each output is given by a Hurwitz polynomial with constant coefficients. Copyright © 2015 John Wiley & Sons, Ltd.

Rogelio Lozano

Papers

Sun Tracking Technique Applied to a Solar Unmanned Aerial Vehicle

Robust adaptive control of a class of nonlinear first order systems

Modeling and control of a lower limb exoskeleton with two degrees of freedom

Singularly perturbed implicit control law for linear time-varying delay MIMO systems

Embedded System for Controlling a Mini Underwater Vehicle in Autonomous Hover Mode