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

In this paper, we present a comparison of three control techniques: Nested Saturations, Backstepping and Sliding Modes. The control objective consists of obtaining the best control strategy to stabilize the position of a quad-rotor when using visual feedback. We propose a method to measure translational speed as well as the UAV 3D position in a local frame. The selected controllers were implemented and tested in real-time experiments. The obtained results demonstrate the performance of such methodologies applied to the quad-rotor system.

/pdf/hovering-quad-rotor-control-a-comparison-of-nonlinear-3elw2476dz.pdf

Hovering quad-rotor control: A comparison of nonlinear controllers using visual feedback

This paper presents recent work concerning a small tiltrotor aircraft with a reduced number of rotors. After several attempts, the final design consists of two propellers mounted laterally. The direction of the thrust can be redirected by tilting the propellers laterally and longitudinally. A theoretical analysis of this mechanism proves its effectiveness and the experimental results show that this aerodynamical configuration is very promising. A model of the full birotor dynamics is also presented in this paper and a controller based on the backstepping procedure is synthesized performing also an autonomous flight.

/pdf/modeling-and-control-of-a-small-autonomous-aircraft-having-kr4cbdbibl.pdf

Modeling and control of a small autonomous aircraft having two tilting rotors

Based on the results of control of the inverted pendulum on a cart, we propose a control law of a convey-crane which transports a load suspended on a cart from a given point to another, minimizing its oscillations. The control law derived is based on the passivity property of the system. Some simulations are presented.

Control of convey-crane based on passivity

This paper describes the design and control algorithm of an original configuration for a small aerial vehicle having three rotors with fixed-pitch propellers. The mechanism of forces and moments generation is described and compared with other vertical take-off and landing (VTOL) vehicles. A mathematical model of the body-forces generation process as well as the 6-DOF (degree of freedom) krotorcraft dynamics is presented. A stabilization algorithm is proposed which takes into account the input amplitude bounds as well as nonlinear couplings in the three-rotor dynamics. The performance of the control strategy is shown in real-time experiments.

Rogelio Lozano

Papers

Hovering quad-rotor control: A comparison of nonlinear controllers using visual feedback

Modeling and control of a small autonomous aircraft having two tilting rotors

Control of convey-crane based on passivity

Real-time stabilization of a small three-rotor aircraft

Adaptive control of a class of nonlinear systems with convex/concave parameterization