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

http://bme2.aut.ac.ir/~towhidkhah/MPC/seminars-ppt/seminar%20MPC/Fazane%20karami/Reference/Architectures%20for%20distributed%20and%20hierarchical%20Model%20Predictive%20Control%20%e2%80%93%20A%20review.pdf

Architectures for distributed and hierarchical Model Predictive Control - A review

https://robotics.nus.edu.sg/sge/journal/switched/automatica-survey-02-2005.pdf

Analysis and synthesis of switched linear control systems

The issue of fundamental limitations in filtering and control lies at the very heart of any feedback system design, since it reveals what is and is not achievable on the basis of that system's structural and dynamic characteristics Alongside new succinct treatments of Bode's original results from the 1940s, this book presents a comprehensive analysis of modern results, featuring contemporary developments in multivariable systems, sampled-data, periodic and nonlinear problems The text gives particular prominence to sensitivity functions which measure the fundamental qualities of the system, including performance and robustness With extensive appendices covering the necessary background on complex variable theory, this book is an ideal self-contained resource for researchers and practitioners in this field

Fundamental Limitations in Filtering and Control

The authors formulate and solve two related control-oriented system identification problems for stable linear shift-invariant distributed parameter plants In each of these problems the assumed a priori information is minimal, consisting only of a lower bound on the relative stability of the plant, an upper bound on a certain gain associated with the plant, and an upper bound on the noise level The first of these problems involves identification of a point sample of the plant frequency response from a noisy, finite, output time series obtained in response to an applied sinusoidal input with frequency corresponding to the frequency point of interest This problem leads naturally to the second problem, which involves identification of the plant transfer function in H/sub infinity / from a finite number of noisy point samples of the plant frequency response Concrete plans for identification algorithms are provided for each of these two problems >

Control oriented system identification: a worst-case/deterministic approach in H/sub infinity /

In this paper, a MIMO interaction measure is described and its use in structure selection of multivariable controllers is discussed. The proposal is built upon a gramian-based measure of interaction in multivariable plants and the results in this paper apply to stable processes. This measure provides support for decentralized input–output pairing as well as for a richer controller architecture selection in continuous and discrete-time time frameworks, including triangular, block diagonal and sparse structures.

MIMO interaction measure and controller structure selection

http://www.nt.ntnu.no/users/skoge/prost/proceedings/ifac2002/data/content/00184/184.pdf

Hankel-norm based interaction measure for input-output pairing

A question which has bothered control researchers for some time is whether hybrid control offers any advantage over linear control for linear plants. We show in this paper, via several examples, that hybrid control can indeed overcome certain types of limitation which are unavoidable if linear feedback control is used.

http://ieeexplore.ieee.org/iel4/4827/13355/00611964.pdf

Potential benefits of hybrid control for linear time invariant plants

Models of physical processes rarely give an exact description of the system's response. Thus an important issue is the quantification of errors in model estimation due to model inadequacy. We show that this problem can be formulated using a Bayesian approach leading to simple formulae for model uncertainty. Techniques for minimizing the amount of computation are also discussed.

Quantification of Uncertainty in Estimation

The goal of this paper is to contribute to the understanding of fundamental performance limits for feedback control systems. In the literature to date on this topic, all available results assume that the designer has an exact model of the plant. Heuristically, however, one would expect that plant uncertainty should play a significant role in determining the best achievable performance. The goal of this paper is to investigate performance limitations for linear feedback control systems in the presence of plant uncertainty. We formulate the problem by utilizing stochastic embedding of the uncertainty. The results allow one to evaluate the best average performance in the presence of uncertainty. They also allow one to judge whether uncertainty or other properties, e.g., nonminimum phase behavior, are dominant limiting factors.

/pdf/performance-limitations-for-linear-feedback-systems-in-the-i6onojpnu9.pdf

Mario E. Salgado

Papers

MIMO interaction measure and controller structure selection

Hankel-norm based interaction measure for input-output pairing

Potential benefits of hybrid control for linear time invariant plants

Quantification of Uncertainty in Estimation

Performance limitations for linear feedback systems in the presence of plant uncertainty