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 global stabilizing control design is proposed for the planar vertical takeoff and landing (PVTOL) aircraft. The methodology is based on the use of nonlinear combinations of saturation functions bounding the thrust input to arbitrary saturation limits. The algorithm is simple and provides global convergence of the state to the origin.

Global stabilization of a PVTOL aircraft with bounded thrust

In this paper, a Lyapunov-based control using singular perturbation theory is proposed and applied on dynamics of a miniature unmanned aerial vehicle (MAV). Such controller is designed taking into account the presence of the small parameter ∈ on vehicle dynamics, causing a time-scale separation between the attitude and translational dynamics of the MAV. The stability analysis is demonstrated by presenting a scenario in which the time-scale property arises on the the MAV dynamics. In addition, the values of the parameter ∈ for which the control law is validated, are given. Simulations are derived an presented to demonstrate the effectiveness of the control law. The proposed controller has been applied to a Quad-plane MAV experimental platform, in order to validate the performance and to show the time-scale property.

/pdf/lyapunov-based-controller-using-singular-perturbation-theory-4s8rmenlwy.pdf

Lyapunov-based controller using singular perturbation theory: An application on a mini-UAV

The aim of this paper is to present the complete model of an unmanned convertible aerial vehicle in hover mode. This vehicle is capable of performing either in hover or in forward flight. A nonlinear control strategy is presented to stabilize the aircraft in hovering mode. An embedded low-cost pilot is described as well the experimental results of a hover flight using a prototype built in the laboratory.

Modelling and Control of a Convertible VTOL Aircraft

In this paper, the coordination and trajectory tracking control design of multiple mini rotorcraft systems are discussed. The dynamic model of a mini rotorcraft is presented using the Newton-Euler formalism. Our approach is based on a leader/follower structure of multiple robot systems. The centroid of the coordinated control subsystem is used for trajectory tracking purposes. A nonlinear coordinated control design for multiple autonomous vehicle synchronization is developed. The analytic results are supported by simulation tests.

/pdf/flight-formation-of-multiple-mini-rotorcraft-via-zhk6t9kbkh.pdf

Flight formation of multiple mini rotorcraft via coordination control

In this paper the problem of bilateral teleoperation is studied for a class of human operator models that are not guaranteed to be passive. Specifically, the hard contact scenario is addressed where the human operator applies a constant force on the master robot and the slave robot interacts with the environment, which is modeled as a spring-damper system. In the delay free case, when the master/slave robots are coupled using the PD control strategy, the nonlinear master-slave teleoperation system is shown to be asymptotically stable. If the environment stiffness is known, then the steady state position of the master and slave robots is predicted. In the case of network delay and for a range of the proportional coupling gains, we demonstrate that the master/slave velocities asymptotically converge to the origin and the positions asymptotically converge to a non-zero equilibrium. Simulations results are also presented to verify the proposed results.

Rogelio Lozano

Papers

Global stabilization of a PVTOL aircraft with bounded thrust

Lyapunov-based controller using singular perturbation theory: An application on a mini-UAV

Modelling and Control of a Convertible VTOL Aircraft

Flight formation of multiple mini rotorcraft via coordination control

Convergence Analysis of Bilateral Teleoperation with Constant Human Input