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

This paper presents the regulation and trajectory tracking for a Micro Coaxial Rocket Helicopter (MCR UAV), as well as the control of a mini aircraft. The former vehicle has the characteristic of performing hover and forward flight while the latter vehicle is considered as an external air transporter for the MCR UAV. For control purposes, the helicopter stabilization is based on sliding mode controllers which avoid the chattering generated during the flight and allow the MCR UAV to perform tracking of smooth trajectories, Furthermore a PD controller stabilizes the aircraft in order to execute semi-autonomous flight. A flight computer for these aerial vehicles consists of a homemade embedded system, low-cost sensors, and signal conditioning circuits, analog filters and actuator. The proposed control algorithms are implemented on the embedded system. Simulation and experimental results show the good performance of the developed system during the flight.

Modeling and Sliding Mode Control of a Micro Helicopter-Airplane System

This paper presents a particular class of a convertible micro aerial vehicle (MAV) with fixed wings, the so-called Quad Tiltrotor aircraft. This aircraft is able to change its flight configuration from hover to level flight and vice versa by means of a transition maneuver. In this first part of the research, the hover dynamics of the Quad Tiltrotor is investigated. Dynamical model and nonlinear control based on Lyapunov design are studied. The presented approach focuses on the problem of finding a control law capable of stabilizing the aircraft's position. Some simulations results are given, which demonstrate the effectiveness of the controller. Further, some experimental results are presented tested on the Quad Tiltrotor experimental platform.

6-DOF hovering controller design of the Quad Tiltrotor aircraft: Simulations and experiments

A real-time localization algorithm is presented in this paper. The algorithm presented here uses an extended Kalman filter and is based on Time Difference Of Arrivals (TDOA) measurements of radio signal. The position and velocity of an Unmanned Aerial Vehicle (UAV) are successfully estimated in closed-loop in real- time, both in hover and path following flights. Relatively small position errors obtained from the experiments prove the good performance of the proposed algorithm.

https://journals.sagepub.com/doi/pdf/10.5772/53748

Rogelio Lozano

Papers

Modeling and Sliding Mode Control of a Micro Helicopter-Airplane System

6-DOF hovering controller design of the Quad Tiltrotor aircraft: Simulations and experiments

Indoor Localization of a Quadrotor Based on WSN: A Real-Time Application:

Design, modeling and stabilization of a multi-rotor helicopter

Stable admittance control without inverse kinematics