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...

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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

This paper deals with the experimental validation of linear controllers for a fixed-wing Miniature Air Vehicle (MAV). We are interested to realize a comparative analysis of two linear controllers, Proportional Integral Derivative (PID) and Proportional Derivative (PD), in order to know what controller has a better performance when they are used on an autonomous flight (altitude, yaw and roll). Experimental results are obtained in order to analyze the controllers and validate the performance of the fixed-wing MAV in presence of perturbations like wind gusts.

Linear controllers implementation for a fixed-wing MAV

This article deals with the design of a novel algorithm that combines a Modified Super-Twisting Controller with a High Order Sliding Mode Observer to enable an aerial vehicle to track a trajectory under the assumption that i) its translational velocities are unavailable and ii) there are unmodeled dynamics and external disturbances. We present a mathematical justification that ensures the existence of a second-order sliding motion for the combination Controller- Observer. In order to demonstrate the effectiveness of the proposed solutions, a set of simulation results are presented.

Robust trajectory tracking for unmanned aircraft systems using high order sliding mode controllers-observers

The authors propose a direct adaptive scheme based on this approach which estimates online the periodic coefficients of the controller. It is shown that adaptive stabilization is attained for all possibly nonstably invertible plants of known order but unknown delay. Although no appeal is made to persistency of excitation arguments, a provision is needed to avoid the singularity of an estimated matrix, this property being required only for the analysis and not the control calculations. >

Adaptive stabilization of discrete-time systems using linear periodically time varying controllers

A fully functional prototype of a gun-launched micro air vehicle system (GLMAV) is developed for long-distance observation capabilities. A subsonic projectile is launched from an ad hoc tube and transforms into a micro air vehicle (MAV) once arrived over the site to be observed. The ballistic, transient, and operational flight phases of the GLMAV are studied theoretically and experimentally in this paper. Ballistic flight tests prove the stability of the platform in projectile mode and the availability of the inertial measurement unit and GPS measurements for the autopilot. Based on wind-tunnel measurements, a model of the transient phase is built, allowing the design and simulation of control laws for this phase. Indoor and outdoor tests of the system are successfully achieved highlighting the hovering and maneuvering flight capabilities of the GLMAV.

Flight Phases With Tests of a Projectile-Drone Hybrid System

We study the extension of what class of linear time invariant plants may be transformed into SPR systems introducing an observer. It is shown that for the open loop stable systems a cascaded observer achieves the result. For the open loop unstable systems an observer-based feedback is required to success. In general any system stabilizable and observable may be transformed into an SPR system. This overcomes the old conditions of minimum phase and relative degree one. The result is illustrated with some examples.

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Rogelio Lozano

Papers

Linear controllers implementation for a fixed-wing MAV

Robust trajectory tracking for unmanned aircraft systems using high order sliding mode controllers-observers

Adaptive stabilization of discrete-time systems using linear periodically time varying controllers

Flight Phases With Tests of a Projectile-Drone Hybrid System

Strictly positive real problem with observers