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

One of the basic questions in control design is how to account for the discrepancies between the model of the plant used for design and the true model. A number of factors may be responsible for modelling errors. A generic term for this modelling error is model uncertainty which can itself be represented mathematically in different ways. Two major classes of uncertainty are: structured uncertainty (or more commonly termed parametric uncertainty) and unstructured uncertainty (usually specified in the frequency domain). The use of unstructured uncertainty description was one of the starting points for the impressive development of robust control design in the 80’s (Zames 1981).

Robust Digital Control Design

In this paper, a teleoperation system for a quadrotor using a virtual environment is presented. A virtual aerial vehicle was introduced by applying the dynamic model of a quadrotor. An attitude controller was implemented for an operator to pilot the drone. The behavior of the virtual drone is communicated to a real vehicle through a mapping between the real and virtual spaces. This mapping is introduced in a robust quaternion-based controller ensures a safe flight in the real world. Simulations and experimental results are carried out to validate the proposal. With this idea of controlling a drone virtually, the performance of beginner and expert drone pilots is improved.

Rogelio Lozano

Papers

Robust Digital Control Design

Teleoperation of a drone based on a virtual environment

Cooperative Control Strategy for an Airplane Landing on a Mobile Target

Performance–guaranteed consensus control inspired by the mammalian limbic system for a class of nonlinear multi-agents

Position Estimation using the Radical Axis Gauss Newton Algorithm: Experimental Analysis