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

A novel underwater vehicle configuration with an operating principle as the Sepiida animal is presented and developed in this paper. The mathematical equations describing the movements of the vehicle are obtained using the Newton–Euler approach. An analysis of the dynamic model is done for control purposes. A prototype and its embedded system are developed for validating analytically and experimentally the proposed mathematical representation. A real-time characterization of one mass is done to relate the pitch angle with the radio of displacement of the mass. In addition, first validation of the closed-loop system is done using a linear controller.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D038CD609426767E36B60F34033B2271/S0263574720000739a.pdf/div-class-title-design-construction-and-control-for-an-underwater-vehicle-type-sepiida-div.pdf

Design, Construction, and Control for an Underwater Vehicle Type Sepiida

The authors wish to reassure the readers that the main result of the above paper, Lozano and Joshi (ibid., vol. 35, no. 11, p. 1243-45, 1990), i.e. Theorem 1, is not questioned in Marquez and Damaren (1995). The authors state that the commenters only question the validity of the proof of Lemma 1, which was a side result and not the main purpose of the paper. The authors agree that the commenters have a valid point which was overlooked in their proof of Lemma 1.3. The authors maintain, however, that Lemma 1 is valid at least in the finite dimensional linear time-invariant (LTI) case, which is the class of systems for which Theorem 1 is applicable. >

Reply to "Comments on 'Strictly positive real transfer functions revisited'"

This paper proposes a simple flying rotor prototype composed of two small airplanes attached to each other with a rigid rod so that they can rotate around themselves. The prototype is intended to perform hover flights with more autonomy than existing classic helicopters or quad-rotors. Given that the two airplanes can fly apart from each other, the induced flow which normally appears in rotorcrafts will be significantly reduced. The issue that is addressed in the paper is how this flying rotor prototype can be modeled and controlled. A model of the prototype is obtained by computing the kinetic and potential energies and applying the Euler Lagrange equations. Furthermore, in order to simplify the equations, it has been considered that the yaw angular displacement evolves much faster than the other variables. Furthermore a study is presented to virtually create a swashplate which is a central mechanism in helicopters. Such virtual swashplate is created by introducing a sinusoidal control on the airplanes’ elevators. The torque amplitude will be proportional to the sinusoidal amplitude and the direction will be determined by the phase of the sinusoidal. A simple nonlinear control algorithm is proposed and its performance is tested in numerical simulations.

Modeling and Control of a Single Rotor Composed of Two Fixed Wing Airplanes

https://onlinelibrary.wiley.com/doi/pdf/10.1002/adc2.22

Two PVTOLs cooperative slung‐load transport control based on passivity

An adaptive control law for PR plants is proposed. The main feature of this approach is that the role of adaptation is not to stabilize the plant but to improve performance. The plant is identified using a standard Least Squares algorithm and through a suitably defined parameter modification, the plant estimates are constrained to a region in the parameter space corresponding to Positive Real Observable Controllable plants. Using these estimates an LQG disipative controller is designed which trivialy stabilizes the plant. Simulation results are presented.

https://ieeexplore.ieee.org/iel7/7055173/7081895/07082083.pdf

Rogelio Lozano

Papers

Design, Construction, and Control for an Underwater Vehicle Type Sepiida

Reply to "Comments on 'Strictly positive real transfer functions revisited'"

Modeling and Control of a Single Rotor Composed of Two Fixed Wing Airplanes

Two PVTOLs cooperative slung‐load transport control based on passivity

Adaptive LQG control of positive real systems