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

Quad Rotorcraft Control develops original control methods for the navigation and hovering flight of an autonomous mini-quad-rotor robotic helicopter. These methods use an imaging system and a combination of inertial and altitude sensors to localize and guide the movement of the unmanned aerial vehicle relative to its immediate environment. The history, classification and applications of UAVs are introduced, followed by a description of modelling techniques for quad-rotor's and the experimental platform itself. A control strategy for the improvement of attitude stabilization in quad-rotor's is then proposed and tested in real-time experiments. The strategy, based on the use low-cost components and with experimentally-established robustness, avoids drift in the UAV's angular position by the addition of an internal control loop to each electronic speed controller ensuring that, during hovering flight, all four motors turn at almost the same speed. The quad-rotor's Euler angles being very close to the origin, other sensors like GPS or image-sensing equipment can be incorporated to perform autonomous positioning or trajectory-tracking tasks. Two vision-based strategies, each designed to deal with a specific kind of mission, are introduced and separately tested. The first stabilizes the quad-rotor over a landing pad on the ground; it extracts the 3-dimensional position using homography estimation and derives translational velocity by optical flow calculation. The second combines colour-extraction and line-detection algorithms to control the quad-rotor's 3-dimensional position and achieves forward velocity regulation during a road-following task. In order to estimate the translational-dynamical characteristics of the quad-rotor (relative position and translational velocity) as they evolve within a building or other unstructured, GPS-deprived environment, imaging, inertial and altitude sensors are combined in a state observer. The text give the reader a current view of the problems encountered in UAV control, specifically those relating to quad-rotor flying machines and it will interest researchers and graduate students working in that field. The vision-based control strategies presented help the reader to a better understanding of how an imaging system can be used to obtain the information required for performance of the hovering and navigation tasks ubiquitous in rotored UAV operation.

Quad Rotorcraft Control: Vision-Based Hovering and Navigation

This note presents some sufficient conditions for a linear system with (point or distributed) delay in the state to be passive. Passivity based (memoryless) stabilization of linear delay systems is also addressed. The proposed approach is based on a Lyapunov-Krasovskii functional construction. Numerical examples are also included.

On the passivity of linear delay systems

Unmanned Aerial Vehicles Embedded Control

Control system design of aerospace vehicles with actuator saturation is an important practical design problem that many previous approaches to nonlinear autopilot design did not consider. In particular, small unmanned aerial vehicle rotorcraft actuators often have physical limitations such as a restricted onboard power supply. Disregard of actuator saturation can affect the final performance, but the reduction in performance can be mitigated if actuator saturation is included in the controller design. In this paper, we propose a nested-saturation-based nonlinear controller for the stabilization of a rotary-wing aircraft. This control strategy allows the incorporation of actuator magnitude saturation and has satisfactory dynamic performance. The nested-saturation technique enables the controller to ensure the global asymptotic stability of a quadrotor helicopter while improving the performance of the closed-loop system. By using Lyapunov analysis, the convergence property is established for the complete nonlinear model of the quadrotor rotorcraft. Simulation results show the performance of the proposed control strategy. Using embedded sensors and onboard control, we performed a real-time autonomous flight. Indeed, experimental results have shown that the proposed control strategy is able to autonomously perform the tasks of taking off, hovering, and landing.

Real-Time Nonlinear Embedded Control for an Autonomous Quadrotor Helicopter

We propose a globally stable finite spectrum assignment adaptive controller for systems with delay. It is assumed that the process is minimum phase, though not necessarily stable, and the delay is known. It is shown that the plant output asymptotically tracks a reference model output with all signals remaining bounded.

Rogelio Lozano

Papers

Quad Rotorcraft Control: Vision-Based Hovering and Navigation

On the passivity of linear delay systems

Unmanned Aerial Vehicles Embedded Control

Real-Time Nonlinear Embedded Control for an Autonomous Quadrotor Helicopter

Globally stable adaptive controller for systems with delay