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

Presents a simple linear periodic controller that achieves semi-global stabilization of linear systems with amplitude constrained inputs. The central scheme is applicable to continuous-time null controllable systems, i.e., systems having open-loop poles in the closed left half-plane.

Semiglobal stabilization of continuous-time systems with bounded inputs

Control of a Gun-Launched MAV for Scene Observation*

The inverted pendulum is a very popular experiment used for educational purposes in modern control theory and this system can appear with different constructions. As we have seen in Chapter 3, the structure of the conventional inverted pendulum is the rail-cart type, which consists of a cart running on a rail and a pendulum attached to the cart. The inverted pendulum of this type has the movement limitation of its cart as a restriction of the control system. On the other hand, the Furuta pendulum has a different structure. It has a direct-drive motor as its actuator source and its pendulum attached to the rotating shaft of the motor. This inverted pendulum on the rotating arm was first developed by K. Furuta at Tokyo Institute of Technology. The product of the experiment was called the TITech pendulum (see [30, 43, 123]).

The Furuta pendulum

The problem of on-line identification of a parametric model for continuous-time, time-varying systems is considered via the minimization of a least-squares criterion with a forgetting function. The proposed forgetting function depends on two time-varying parameters which play crucial roles in the stability analysis of the method. The analysis leads to the consideration of a Lyapunov function for the identification algorithm that incorporates both prediction error and parameter convergence measures. A theorem is proved showing finite time convergence of the Lyapunov function to a neighbourhood of zero, the size of which depends on the evolution of the time-varying error terms in the parametric model representation. Copyright © 2001 John Wiley & Sons, Ltd.

Generalized forgetting functions for on‐line least‐squares identification of time‐varying systems

This paper presents an adaptive control scheme for first order systems of the form y + a*y = b* 0 u + b* 1 u which may possibly be nonminimum phase. The control scheme achieves asymptotical stabilization without any apriori knowledge on the plant parameters. The adaptive scheme is free from singularities in the sense that the plant estimated model is always controllable. The singularity has been overcome through a suitable modification of the parameters estimates which is based on standard least squares covariance matrix properties.

Rogelio Lozano

Papers

Semiglobal stabilization of continuous-time systems with bounded inputs

Control of a Gun-Launched MAV for Scene Observation*

The Furuta pendulum

Generalized forgetting functions for on‐line least‐squares identification of time‐varying systems

Adaptive Stabilization of Nonminimum Phase First Order Continuous-Time Systems