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 book, written by two major figures in adaptive control, provides a wealth of material for researchers, practitioners, and students. While some researchers in adaptive control may note the absence of a particular topic, the book‘s scope represents a high-gain instrument. It can be used by designers of control systems to enhance their work through the information on many new theoretical developments, and can be used by mathematical control theory specialists to adapt their research to practical needs. The book is strongly recommended to anyone interested in adaptive control.

Adaptive Control

Nonlinear Oscillations: Exact Solutions and their Approximations

Thank you very much for downloading introduction to infinite dimensional linear systems theory. As you may know, people have search numerous times for their favorite novels like this introduction to infinite dimensional linear systems theory, but end up in malicious downloads. Rather than enjoying a good book with a cup of tea in the afternoon, instead they juggled with some harmful bugs inside their laptop.

Introduction To Infinite Dimensional Linear Systems Theory

http://flyingv.ucsd.edu/papers/PDF/123.pdf

Brief paper: Adaptive trajectory tracking despite unknown input delay and plant parameters

Adaptive control scheme for uncertain time-delay systems

Stabilization of an unstable system with an unknown actuator delay of substantial length is an important problem that has never been attempted. We present a Lyapunov-based adaptive control design, prove its stability and regulation properties for the plant and actuator states, and present a simulation example inspired by the problem of control of pitch and flight path rates in the unstable X-29 aircraft.

/pdf/delay-adaptive-predictor-feedback-for-systems-with-unknown-1grbe0gxrd.pdf

Delay-Adaptive Predictor Feedback for Systems With Unknown Long Actuator Delay $ $

Stabilization of an unstable system with an unknown actuator delay of substantial length is an important problem that has never been attempted. We present a Lyapunov-based adaptive control design, prove its stability and regulation properties for the plant and actuator states, and present a simulation example inspired by the problem of control of pitch and flight path rates in the unstable X-29 aircraft. Index Terms—Adaptive control, delay systems, distributed parameter systems.

https://ieeexplore.ieee.org/iel5/9/5565431/05464336.pdf

Technical Notes and Correspondence Delay-Adaptive Predictor Feedback for Systems With Unknown Long Actuator Delay

We present a systematic delay-adaptive prediction-based control design for nonlinear systems with unknown long actuator delay. Our approach is based on the representation of the constant actuator delay as a transport Partial Differential Equation (PDE) in which the convective speed is inversely proportional to the unknown delay. We study two different frameworks, assuming first that the actuator state is measured and relaxing afterward. For the full-state feedback case, we prove global asymptotic convergence of the proposed adaptive controller while, in the second case, replacing the actuator state by its adaptive estimate, we prove local regulation. The relevance of the obtained results are illustrated by simulations of a biological activator/repressor system.

Delphine Bresch-Pietri

Papers

Brief paper: Adaptive trajectory tracking despite unknown input delay and plant parameters

Adaptive control scheme for uncertain time-delay systems

Delay-Adaptive Predictor Feedback for Systems With Unknown Long Actuator Delay $ $

Technical Notes and Correspondence Delay-Adaptive Predictor Feedback for Systems With Unknown Long Actuator Delay

Delay-Adaptive Control for Nonlinear Systems