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 short paper we consider the adaptive control of multivariable discrete time minimum phase systems. The system under consideration is not supposed to be decouplable by static state feedback. The adaptive control design presented here is based on pole zero placement. The a priori knowledge of the plant transfer matrix Hermite form is not necessary, this knowledge is replaced by that of the largest infinite zero order of the plant transfer matrix.

An indirect adaptive control scheme for mimo systems

This paper presents the mathematical model of a fixed wing mini-UAV (Unmanned Aerial Vehicle). The mini-UAV is not a tail-sitter configuration and takes-off with the fuselage at the horizontal position. An experimental prototype driven by four brushless motors has been built including the onboard avionics. The applied control law is based on separated saturation functions algorithm. Numerical simulations have shown the satisfactory performance of the proposed control law in vertical take-off and hover. The prototype has also been tested experimentally in hover only and the control strategy has achieved that orientation angles have been regulated close to the origin.

Modeling and control of a convertible airplane

Stabilization of the planar vertical take-off and landing using nonlinear feedback control

Nonlinear Control and Trajectory Tracking of an Unmanned Aircraft System Based on a Complete State Space Representation

A new indirect adaptive control method is presented. This method is based on a lifted representation of the plant which can be stabilized using a simple periodic control scheme. The controller parameter computation involves the inverse controllability/observability matrix. Potential singularities of this matrix are avoided by means of an appropriate estimate modification. This estimate transformation is linked to the covariance matrix properties and hence it preserves the convergence properties of the original estimates. This modification involves the singular value decomposition of the controllability/observability matrix estimate. As compared to previous studies in the subject the controller proposed here does not require the frequent introduction of periodic n-length sequences of zero inputs. Thus with the new controller the system is almost always operating in a closed loop, which should lead to better performance characteristics.

Rogelio Lozano

Papers

An indirect adaptive control scheme for mimo systems

Modeling and control of a convertible airplane

Stabilization of the planar vertical take-off and landing using nonlinear feedback control

Nonlinear Control and Trajectory Tracking of an Unmanned Aircraft System Based on a Complete State Space Representation

Indirect adaptive periodic control