Robust control of systems with real parameter uncertainty and unmodelled dynamics

Two significant contributions have been made during this research period in the research 'Robust Control of Systems with Real Parameter Uncertainty and Unmodelled Dynamics' under NASA Research Grant NAG-1-1102. They are: (1) a fast algorithm for computing the optimal H(sub infinity) norm for the four-block, the two block, or the one-block optimal H(sub infinity) optimization problem; and (2) a construction of an optimal H infinity controller without numerical difficulty. In using GD (Glover and Doyle) or DGKF (Doyle, Glover, Khargonekar, and Francis) approach to solve the standard H infinity norm which required bisection search. In this research period, we developed a very fast iterative algorithm for this computation. Our algorithm was developed based on hyperbolic interpolations which is much faster than any existing algorithm. The lower bound of the parameter, gamma, in the H infinity Riccati equation for solution existence is shown to be the square root of the supremum over all frequencies of the maximum eigenvalue of a given transfer matrix which can be computed easily. The lower band of gamma such that the H infinity Riccati equation has positive semidefinite solution can be also obtained by hyperbolic interpolation search. Another significant result in this research period is the elimination of the numerical difficulties arising in the construction of an optimal H infinity controller by directly applying the Glover and Doyle's state-space formulas. With the fast iterative algorithm for the computation of the optimal H infinity norm and the reliable construction of an optimal H infinity controller, we are ready to apply these tools in the design of robust controllers for the systems with unmodelled uncertainties. These tools will be also very useful when we consider systems with structured uncertainties

Robust control of systems with real parameter uncertainty and unmodelled dynamics

During this research period we have made significant progress in the four proposed areas: (1) design of robust controllers via H infinity optimization; (2) design of robust controllers via mixed H2/H infinity optimization; (3) M-delta structure and robust stability analysis for structured uncertainties; and (4) a study on controllability and observability of perturbed plant. It is well known now that the two-Riccati-equation solution to the H infinity control problem can be used to characterize all possible stabilizing optimal or suboptimal H infinity controllers if the optimal H infinity norm or gamma, an upper bound of a suboptimal H infinity norm, is given. In this research, we discovered some useful properties of these H infinity Riccati solutions. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma in the domain of interest. Based on these properties, quadratically convergent algorithms are developed to compute the optimal H infinity norm. We also set up a detailed procedure for applying the H infinity theory to robust control systems design. The desire to design controllers with H infinity robustness but H(exp 2) performance has recently resulted in mixed H(exp 2) and H infinity control problem formulation. The mixed H(exp 2)/H infinity problem have drawn the attention of many investigators. However, solution is only available for special cases of this problem. We formulated a relatively realistic control problem with H(exp 2) performance index and H infinity robustness constraint into a more general mixed H(exp 2)/H infinity problem. No optimal solution yet is available for this more general mixed H(exp 2)/H infinity problem. Although the optimal solution for this mixed H(exp 2)/H infinity control has not yet been found, we proposed a design approach which can be used through proper choice of the available design parameters to influence both robustness and performance. For a large class of linear time-invariant systems with real parametric perturbations, the coefficient vector of the characteristic polynomial is a multilinear function of the real parameter vector. Based on this multilinear mapping relationship together with the recent developments for polytopic polynomials and parameter domain partition technique, we proposed an iterative algorithm for coupling the real structured singular value

Real-Time Anisotropic Diffusion using Space-Variant Vision

Many computer and robot vision applications require multi-scale image analysis. Classically, this has been accomplished through the use of a linear scale-space, which is constructed by convolution of visual input with Gaussian kernels of varying size (scale). This has been shown to be equivalent to the solution of a linear diffusion equation on an infinite domain, as the Gaussian is the Green's function of such a system (Koenderink, 1984). Recently, much work has been focused on the use of a variable conductance function resulting in anisotropic diffusion described by a nonlinear partial differential equation (PDF). The use of anisotropic diffusion with a conductance coefficient which is a decreasing function of the gradient magnitude has been shown to enhance edges, while decreasing some types of noise (Perona and Malik, 1987). Unfortunately, the solution of the anisotropic diffusion equation requires the numerical integration of a nonlinear PDF which is a costly process when carried out on a fixed mesh such as a typical image. In this paper we show that the complex log transformation, variants of which are universally used in mammalian retino-cortical systems, allows the nonlinear diffusion equation to be integrated at exponentially enhanced rates due to the non-uniform mesh spacing inherent in the log domain. The enhanced integration rates, coupled with the intrinsic compression of the complex log transformation, yields a seed increase of between two and three orders of magnitude, providing a means of performing real-time image enhancement using anisotropic diffusion.Office of Naval Research (N00014-95-I-0409

A monitor for the laboratory evaluation of control integrity in digital control systems operating in harsh electromagnetic environments

This paper presents a strategy for dynamically monitoring digital controllers in the laboratory for susceptibility to electromagnetic disturbances that compromise control integrity. The integrity of digital control systems operating in harsh electromagnetic environments can be compromised by upsets caused by induced transient electrical signals. Digital system upset is a functional error mode that involves no component damage, can occur simultaneously in all channels of a redundant control computer, and is software dependent. The motivation for this work is the need to develop tools and techniques that can be used in the laboratory to validate and/or certify critical aircraft controllers operating in electromagnetically adverse environments that result from lightning, high-intensity radiated fields (HIRF), and nuclear electromagnetic pulses (NEMP). The detection strategy presented in this paper provides dynamic monitoring of a given control computer for degraded functional integrity resulting from redundancy management errors, control calculation errors, and control correctness/effectiveness errors. In particular, this paper discusses the use of Kalman filtering, data fusion, and statistical decision theory in monitoring a given digital controller for control calculation errors

Transformations in the Carpathian Basin around 1600 B. C.

Um die Zeit des Vulkanausbruchs von Thera fanden wichtige Veränderungen im Karpatenbecken statt. Diese sogenannte Koszider Epoche korrespondiert mit der letzten Phase der mittleren Bronzezeit in der ungarischen Terminologie und stellt den Übergang zur späten Bronzezeit dar. Die Untersuchung dieser Epoche hat sich bisher als kontrovers erwiesen – sowohl unter ungarischen als auch mitteleuropäischen Wissenschaftlern. Erst in den letzten Jahren ist diese Epoche nicht mehr als kurzer Zeitraum, mit der ein bestimmtes historisches Ereignis verbunden werden kann, interpretiert worden. Vielmehr sieht man sie nun als eine länger dauernde Periode an, welche die Blütezeit der mittleren Bronzezeit im Karpatenbecken markiert und die mit einschneidenden Veränderungen endet. Die Hauptelemente dieses Wandels sind allerdings noch unklar. Unser Ziel ist es, den Wandel durch den Vergleich verschiedener Aspekte dreier aufeinanderfolgender Phasen zu untersuchen. Am Ende sollen einige neue Erwägungen stehen, die die bisherigen Interpretationen dieser Veränderungen erweitern können. | Around the time of the Thera eruption important transformations occurred in the Carpathian Basin. This is the so-called Koszider Period, which corresponds to the last phase of the Middle Bronze Age (MBA) in the Hungarian terminology and represents a transition to the Late Bronze Age. The assessment of the period has been controversial among both Hungarian and central European scholars. In the past few years this period has been interpreted not as a short »horizon« connected to a specific historical event, but as a longer period that represented the heyday of the MBA in the Carpathian Basin, which ended with significant transformations. The main elements of this transformation, however, are still unclear. Our aim is to investigate this transformation through the comparison of several aspects of three subsequent phases and to amend the previously offered interpretations of the changes with a few new considerations

Adaptive Nonlocal Filtering: A Fast Alternative to Anisotropic Diffusion for Image Enhancement

The goal of many early visual filtering processes is to remove noise while at the same time sharpening contrast. An historical succession of approaches to this problem, starting with the use of simple derivative and smoothing operators, and the subsequent realization of the relationship between scale-space and the isotropic dfffusion equation, has recently resulted in the development of "geometry-driven" dfffusion. Nonlinear and anisotropic diffusion methods, as well as image-driven nonlinear filtering, have provided improved performance relative to the older isotropic and linear diffusion techniques. These techniques, which either explicitly or implicitly make use of kernels whose shape and center are functions of local image structure are too computationally expensive for use in real-time vision applications. In this paper, we show that results which are largely equivalent to those obtained from geometry-driven diffusion can be achieved by a process which is conceptually separated info two very different functions. The first involves the construction of a vector~field of "offsets", defined on a subset of the original image, at which to apply a filter. The offsets are used to displace filters away from boundaries to prevent edge blurring and destruction. The second is the (straightforward) application of the filter itself. The former function is a kind generalized image skeletonization; the latter is conventional image filtering. This formulation leads to results which are qualitatively similar to contemporary nonlinear diffusion methods, but at computation times that are roughly two orders of magnitude faster; allowing applications of this technique to real-time imaging. An additional advantage of this formulation is that it allows existing filter hardware and software implementations to be applied with no modification, since the offset step reduces to an image pixel permutation, or look-up table operation, after application of the filter

Social Network Intelligence Analysis to Combat Street Gang Violence

In this paper we introduce the Organization, Relationship, and Contact Analyzer (ORCA) that is designed to aide intelligence analysis for law enforcement operations against violent street gangs. ORCA is designed to address several police analytical needs concerning street gangs using new techniques in social network analysis. Specifically, it can determine "degree of membership" for individuals who do not admit to membership in a street gang, quickly identify sets of influential individuals (under the tipping model), and identify criminal ecosystems by decomposing gangs into sub-groups. We describe this software and the design decisions considered in building an intelligence analysis tool created specifically for countering violent street gangs as well as provide results based on conducting analysis on real-world police data provided by a major American metropolitan police department who is partnering with us and currently deploying this system for real-world use

On the formulation of a minimal uncertainty model for robust control with structured uncertainty

In the design and analysis of robust control systems for uncertain plants, representing the system transfer matrix in the form of what has come to be termed an M-delta model has become widely accepted and applied in the robust control literature. The M represents a transfer function matrix M(s) of the nominal closed loop system, and the delta represents an uncertainty matrix acting on M(s). The nominal closed loop system M(s) results from closing the feedback control system, K(s), around a nominal plant interconnection structure P(s). The uncertainty can arise from various sources, such as structured uncertainty from parameter variations or multiple unsaturated uncertainties from unmodeled dynamics and other neglected phenomena. In general, delta is a block diagonal matrix, but for real parameter variations delta is a diagonal matrix of real elements. Conceptually, the M-delta structure can always be formed for any linear interconnection of inputs, outputs, transfer functions, parameter variations, and perturbations. However, very little of the currently available literature addresses computational methods for obtaining this structure, and none of this literature addresses a general methodology for obtaining a minimal M-delta model for a wide class of uncertainty, where the term minimal refers to the dimension of the delta matrix. Since having a minimally dimensioned delta matrix would improve the efficiency of structured singular value (or multivariable stability margin) computations, a method of obtaining a minimal M-delta would be useful. Hence, a method of obtaining the interconnection system P(s) is required. A generalized procedure for obtaining a minimal P-delta structure for systems with real parameter variations is presented. Using this model, the minimal M-delta model can then be easily obtained by closing the feedback loop. The procedure involves representing the system in a cascade-form state-space realization, determining the minimal uncertainty matrix, delta, and constructing the state-space representation of P(s). Three examples are presented to illustrate the procedure

PSACNN: Pulse Sequence Adaptive Fast Whole Brain Segmentation

With the advent of convolutional neural networks~(CNN), supervised learning methods are increasingly being used for whole brain segmentation. However, a large, manually annotated training dataset of labeled brain images required to train such supervised methods is frequently difficult to obtain or create. In addition, existing training datasets are generally acquired with a homogeneous magnetic resonance imaging~(MRI) acquisition protocol. CNNs trained on such datasets are unable to generalize on test data with different acquisition protocols. Modern neuroimaging studies and clinical trials are necessarily multi-center initiatives with a wide variety of acquisition protocols. Despite stringent protocol harmonization practices, it is very difficult to standardize the gamut of MRI imaging parameters across scanners, field strengths, receive coils etc., that affect image contrast. In this paper we propose a CNN-based segmentation algorithm that, in addition to being highly accurate and fast, is also resilient to variation in the input acquisition. Our approach relies on building approximate forward models of pulse sequences that produce a typical test image. For a given pulse sequence, we use its forward model to generate plausible, synthetic training examples that appear as if they were acquired in a scanner with that pulse sequence. Sampling over a wide variety of pulse sequences results in a wide variety of augmented training examples that help build an image contrast invariant model. Our method trains a single CNN that can segment input MRI images with acquisition parameters as disparate as $T_1$-weighted and $T_2$-weighted contrasts with only $T_1$-weighted training data. The segmentations generated are highly accurate with state-of-the-art results~(overall Dice overlap$=0.94$), with a fast run time~($\approx$ 45 seconds), and consistent across a wide range of acquisition protocols.Comment: Typo in author name corrected. Greves -> Grev

Ároktő-Dongóhalom középső bronzkori települése és tájtörténet a Bükk és az Alföld találkozásánál = Ároktő-Dongóhalom (middle Bronze Age settlement) and the landscape history of the Bükk Mountains/Great Hungarian Plain juncture

Kutatómunkám egyik célja az Ároktő-dongóhalmi bronzkori tell település Megay Géza (1930) és Kemenczei Tibor (1966) vezette ásatásai leletanyagának feldolgozása (leltározás, tipokronológia és településtörténet). A település legalsó rétege a hatvan-kultúra korai fázisának (RBA1) leleteit szolgáltatta. Ezt a réteget egy széles, mély árok vette körül. A felső három réteg leletanyaga a füzesabonyi kultúrába sorolható. A két kultúra települési rétegei között feltehetően planírozási, tereprendezési munkák nyomait figyelhetjük meg (árokfeltöltés, 1. szelvény metszetfalában 70 cm-es feltöltési szint). Az 1930-as és 1966-os leletanyagot a füzesabonyi kultúra klasszikus, késői, klasszikus fázisába sorolhatjuk, mint a névadó füzesabonyi telep felső három rétege, a pusztaszikszói és a geleji sírok időszaka, Bárca II rétege és az alsómislyei telep klasszikus füzesabonyi korszakba sorolható része. A bodrogszerdahelyi fázis edényművességének fő jellemzői nem találhatók meg jelentős mennyiségben a leletanyagban. A kutatómunka másik célja a Borsodi Mezőség területén (Hejő, Tisza és Kánya folyók által határolt terület) bronzkori településhálózat rekonstruálása. Erre a célra kéziratos és történeti térképeket, archív légifényképeket, régészeti szakadatokat és terepbejárás adatait térinformatikai rendszerbe illesztettük. Az így létrejött adatbázist összehasonlítottuk az ároktői leletanyag konkrét tipológiai adataival. | One objective of my survey was to investigate the findings (inventory, typochronology and settlement history) of the excavations carried out by Megay, Géza (1930) and Kemenczei, Tibor (1966) at a Bronze-Age tell settlement, Ároktő-Dongóhalom. Finds from the early stage of Hatvan community (RBA1) were explored from the lower settlement layer. This layer was bordered with a wide, deep ditch. Finds from the upper 3 strata belong to the Füzesabony-Culture. The two settlement phase bear the marks of various surface works. The 1930 and 1966 find assemblage can be dated to the classical and late classical phase of the Füzesabony culture, similarly to the uppermost three levels of the epnymous Füzesabony settlement, the Pusztaszikszó and the Gelej burials, layer II of the Barca settlement and the classical Füzesabony period levels of the Ny?na Mi?la settlement. The finds presented hardly contain any finds betraying the pottery traits of the Streda nad Bodrogom-Phase. Another objective of the programme was to reconstruct the Bronze-age settlement structure of a smaller region in Borsodi Mezőség (delineated by Hejő stream, Tisza river and Kánya stream). Manuscripts and historic maps, archive aerial photographs, archeological, technical data and findings of field surveys were processed with GIS applications, and the Bronze-age settlement structure of the area was defined. This description was compared to the concrete typological data of the Ároktő sites