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 article addresses the development and experimental validation of a trajectory-tracking control for a miniature autonomous Quadrotor helicopter system (X4-prototype) using a robust algorithm control based on second-order sliding mode technique or also known as super-twisting algorithm in outdoor environments. This nonlinear control strategy guarantees the convergence in finite time to a desired path r(t) in the presence of external disturbances or uncertainties in the model affecting the appropriate behavior of our Quadrotor helicopter. For this purpose, a polynomial smooth curve trajectory is selected as a reference signal where the corresponding derivatives of the function are bounded. Moreover, we consider disturbances due to wind gusts acting on the aerial vehicle, and the reference signal is pre-programmed in an advanced autopilot system. The proposed solution consists of implementing a real-time control law based on super-twisting control using GPS measurements in order to obtain the position in the xy-plane to accomplish the desired trajectory. Simulation and experimental results of trajectory-tracking control are presented to demonstrate the performance and robustness of the proposed nonlinear controller in windy conditions.

/pdf/real-time-improvement-of-a-trajectory-tracking-control-based-3joma921.pdf

Real-Time Improvement of a Trajectory-Tracking Control Based on Super-Twisting Algorithm for a Quadrotor Aircraft

Real Time Parameter Identification of the Inertia Tensor for a Quad-rotor mini-aircraft using Adaptive Control

The inverted pendulum is one of the most popular laboratory experiments used for illustrating non-linear control techniques. This system is motivated by applications such as the control of rockets and the antiseismic control of buildings.

The cart-pole system

The present paper addresses the transition stage of a Gun-Launched Micro Air Vehicle (GLMAV) whose main goal is to rapidly position a rotorcraft MAV over a high-risk scene (Prison riots, blind zones: e.g. over-the-hill, etc.). The development of this robotic platform is part of an overall ongoing project (GLMAV) headed by the St. Louis French-German Research Institute (ISL). The vehicle is launched at a distance of 500 m and a height of 100 m, where the GLMAV will collect and transmit visual information from the scene. Issues raising from the use of the gun-based launching technique are discussed in detail. A control strategy is proposed to overcome such problems and to stabilize the GLMAV. High-fidelity simulations, covering ballistic and transition phases, validate the control policy adopted to face the MAV gun-launching problem.

/pdf/the-transition-phase-of-a-gun-launched-micro-air-vehicle-ubfiyms1lm.pdf

The Transition Phase of a Gun-Launched Micro Air Vehicle

Estimating position and orientation (pose) of an object in real time constitutes an important issue for vision-based control of robots. In this paper, we present a nonlinear controller design based on vision and its application in a quadrotor. Experiment results show good performance of the proposed controller using “real-time” optical flow and image processing.

Rogelio Lozano

Papers

Real-Time Improvement of a Trajectory-Tracking Control Based on Super-Twisting Algorithm for a Quadrotor Aircraft

Real Time Parameter Identification of the Inertia Tensor for a Quad-rotor mini-aircraft using Adaptive Control

The cart-pole system

The Transition Phase of a Gun-Launched Micro Air Vehicle

Stabilization of a helicopter using optical flow