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

Dissipative Systems Analysis and Control

In this paper, we present a controller design and its implementation on a mini rotorcraft having four rotors. The dynamic model of the four-rotor rotorcraft is obtained via a Lagrange approach. The proposed controller is based on Lyapunov analysis using a nested saturation algorithm. The global stability analysis of the closed-loop system is presented. Real-time experiments show that the controller is able to perform autonomously the tasks of taking off, hovering, and landing.

Real-time stabilization and tracking of a four-rotor mini rotorcraft

Dissipative Systems Analysis and Control (second edition) presents a fully revised and expanded treatment of dissipative systems theory, constituting a self-contained, advanced introduction for graduate students, researchers and practising engineers. It examines linear and nonlinear systems with examples of both in each chapter; some infinite-dimensional examples are also included. Throughout, emphasis is placed on the use of the dissipative properties of a system for the design of stable feedback control laws. The theory is substantiated by experimental results and by reference to its application in illustrative physical cases (Lagrangian and Hamiltonian systems and passivity-based and adaptive controllers are covered thoroughly). The second edition is substantially reorganized both to accommodate new material and to enhance its pedagogical properties. Some of the changes introduced are: * Complete proofs of the main theorems and lemmas. * The Kalman-Yakubovich-Popov Lemma for non-minimal realizations, singular systems, and discrete-time systems (linear and nonlinear). * Passivity of nonsmooth systems (differential inclusions, variational inequalities, Lagrangian systems with complementarity conditions). * Sections on optimal control and H-infinity theory. * An enlarged bibliography with more than 550 references, and an augmented index with more than 500 entries. * An improved appendix with introductions to viscosity solutions, Riccati equations and some useful matrix algebra.

Dissipative Systems Analysis and Control: Theory and Applications

From the Publisher:
This book deals with the application of modern control theory to some important underactuated mechanical systems. It presents modelling and control of the following systems:||- the inverted pendulum||- a convey-crane system||- the pendubot system||- the Furuta pendulum||- the inertia wheel pendulum||- the planar flexible-joint robot||- the planar manipulator with two prismatic and one revolute joints||- the ball & beam system||- the hovercraft model||- the planar vertical and take-off landing (PVTOL) aircraft||- the helicopter model on a platform||- the helicopter model||In every case the model is obtained in detail using either the Euler-Lagrange formulation or the Newton's second law. We develop control algorithms for every particular system using techniques such as passivity, energy-based Lyapunov functions, forwarding, backstepping or feedback linearization techniques.||This book will be of great value for PhD students and researchers in the areas of non-linear control systems.

Non-linear Control for Underactuated Mechanical Systems

Modelling and Control of Mini-Flying Machinesis an exposition of models developed to assist in the motion control of various types of mini-aircraft: Planar Vertical Take-off and Landing aircraft; helicopters; quadrotor mini-rotorcraft; other fixed-wing aircraft; blimps. For each of these it propounds: detailed models derived from Euler-Lagrange methods; appropriate nonlinear control strategies and convergence properties; real-time experimental comparisons of the performance of control algorithms; review of the principal sensors, on-board electronics, real-time architecture and communications systems for mini-flying machine control, including discussion of their performance; detailed explanation of the use of the Kalman filter to flying machine localization. To researchers and students in nonlinear control and its applications Modelling and Control of Mini-Flying Machines provides valuable insights to the application of real-time nonlinear techniques in an always challenging area.

https://www.springer.com/productFlyer_978-1-85233-957-9.pdf?SGWID=0-0-1297-39145381-0

Rogelio Lozano

Papers

Dissipative Systems Analysis and Control

Real-time stabilization and tracking of a four-rotor mini rotorcraft

Dissipative Systems Analysis and Control: Theory and Applications

Non-linear Control for Underactuated Mechanical Systems

Modelling and Control of Mini-Flying Machines