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 this chapter we shall present a class of dissipative systems which correspond to models of physical systems and hence embed in their structure the conservation of energy (first principle of thermodynamics) and the interaction with their environment through pairs of conjugated variables with respect to the power. Firstly, we shall recall three different definitions of systems obtained by an energy based modeling: controlled Lagrangian, input-output Hamiltonian systems and port controlled Hamiltonian systems. We shall illustrate and compare these definitions on some very simple examples. Secondly we shall treat a class of systems which gave rise to numerous stabilizing control using passivity theory and corresponds to models of robotic manipulators. In each worked case we show how the main functions associated to a dissipative system (the available storage, the required supply, storage functions) can be computed analytically and related to the energy of the physical system.

Dissipative Physical Systems

This paper addresses the problem of autonomous navigation of a quadrotor helicopter using state estimators when the GPS signal is not available. The main objective is to estimate the translational position and velocity of the flying machine. The observer proposed uses a double integral approximation of the acceleration defined in the mathematical model in order to estimate the states previously mentioned. To apply this approach, a recursive least squares algorithm is programmed to get better estimations. Real-time experiments have been conducted in order to verify the validity and effectiveness of the proposed estimation approach, and the obtained results are presented and discussed.

Estimation of velocity and position for a quadrotor aircraft in GPS denied environment

Most kite wind power systems have a great drawback that wind turbines do not have: they cannot stay in the air if the wind is not strong enough, [7-16]. As a consequence, most of the kite systems need to land when there is no wind, and to take-off once the wind is strong enough. These maneuvers are quite risky because generally the wind gets weak and turbulent close to the ground's surface. Moreover, as the wind can be strong enough at high altitude and weak close to the ground, it might lead to losses in energy production. From a material point of view, “classic” landings and takeoffs need a landing zone, ground handling or infrastructure (such as pylons) that reduces the advantages of kite systems. Some ideas, such as embedded motors or helium balloons, might solve this problem, but they have their own drawbacks such as the weight of the motor and its battery, the necessity of a conductive cable or the need to refill the balloons. The following paper studies a solution called “reverse pumping”. It basically consists of providing kinetic energy to the kite by pulling the kite with a rope. This kinetic energy is then transformed into potential energy by gaining altitude. This technique allows to keep the kite airborne in total absence of wind. This paper will study the reverse pumping principle, the constrains on the aerodynamical model, flight simulations and will present the experimental setup used to validate the theoretical study.

/pdf/reverse-pumping-theory-and-experimental-validation-on-a-s64m0izwqx.pdf

Reverse pumping: Theory and experimental validation on a multi-kites system

An integral robust observer with rejection control disturbance is proposed in this paper. The design of the observer is performed employing the canonical obervable model of the original non-linear system, obtained by a change of coordinates. A practical stability is proved using the Lyapunov approach with using a high gain to maintain the solution in a convergence ball. Several simulations cases are carried out to illustrate the performance of the closed-loop system in a disturbance wind prepense. In other cases, noise in the states are added to emulate a real system.

http://ieeexplore.ieee.org/iel7/7436433/7440980/07441035.pdf

Robust control with disturbance observer for UAV translational tracking

The two-link underactuated robotic mechanism called the pendubot is used for research in non-linear control and for education in various concepts like non-linear dynamics, robotics and control system design.

Rogelio Lozano

Papers

Dissipative Physical Systems

Estimation of velocity and position for a quadrotor aircraft in GPS denied environment

Reverse pumping: Theory and experimental validation on a multi-kites system

Robust control with disturbance observer for UAV translational tracking

The pendubot system