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 paper a simple control algorithm to stabilize the attitude of a quad-rotor aircraft is presented. The controller is obtained using the backstepping technique and adding saturation functions. The analysis of convergence is carried out by using the Lyapunov analysis. The performance of the controller with respect to a classical PD controller is compared by simulation. The robustness of the control algorithm with respect to aggressive perturbations is illustrated with real-time experiments.

Simple Real-time Attitude Stabilization of a Quad-rotor Aircraft With Bounded Signals

http://www.nt.ntnu.no/users/skoge/prost/proceedings/ifac2008/data/papers/0082.pdf

Asymptotic Stability of Hierarchical Inner-Outer Loop-Based Flight Controllers

The goal of this paper is to present a novel configuration for a three-rotor mini unmanned aerial vehicle (UAV). The proposed design incorporates advantageous structural features which enhance the maneuverability of the rotorcraft. The detailed mathematical model of the vehicle's attitude is obtained through the Newton-Euler formulation. In terms of control, we propose a control law which is robust with respect to dynamical couplings and adverse torques. The vehicle tilts simultaneously the three rotors to stabilize the yaw dynamics. The resulting control algorithm is simple for embedded purposes. A customized low-cost embedded system was developed to test an autonomous stabilized-attitude flight, obtaining satisfactory results.

/pdf/triple-tilting-rotor-mini-uav-modeling-and-embedded-control-vx75tfccv0.pdf

Triple tilting rotor mini-UAV: Modeling and embedded control of the attitude

Brief Robust adaptive identification of slowly time-varying parameters with bounded disturbances

This paper deals with the design of four controllers, based on Backstepping and Sliding Modes, which are applied to a fixed-wing unmanned aerial vehicle (UAV). We are interested to realize a comparative analysis of such methodologies in order to know what controller has a better performance when they are used to the autonomous flight (altitude, yaw and roll) of a fixed-wing UAV. The designed controllers are: Backstepping, sliding mode control (SMC), Backstepping with sliding mode control, and Backstepping with two sliding mode control. Simulation results are obtained in order to analyze the controllers. We finally present an experimental result, in open-loop, with the purpose of validate the magnitud of the control signals obtained in the simulations.

Rogelio Lozano

Papers

Simple Real-time Attitude Stabilization of a Quad-rotor Aircraft With Bounded Signals

Asymptotic Stability of Hierarchical Inner-Outer Loop-Based Flight Controllers

Triple tilting rotor mini-UAV: Modeling and embedded control of the attitude

Brief Robust adaptive identification of slowly time-varying parameters with bounded disturbances

Backstepping — Sliding mode controllers applied to a fixed-wing UAV