Allen Tannenbaum - US grants

The general problem of robust system control consists of constructing fixed feedback controllers for possibly unstable families of systems with parameter or modelling uncertainty in order to stabilize the given family and in order to meet certain performance specifications. This proposal is concerned with an operator theoretic and functional analytic approach to this problem for multivariable, distributed, and even possibly nonlinear plants. Specifically, techniques will be proposed to solve the H-Infinity-optimal weighted sensitivity problem for multivariate distributed systems, and methods will be developed for obtaining new qualitative and quantitive results for very general multivariable gain margin problems. Moreover, a nonlinear version of classical interpolation theory will be considered and it should have important consequences in adaptive and robust nonlinear control. It is expected that the proposed operator theoretic approach should help resolve some fundamental problems in robust design and illuminate a number of central theoretical issues in this area. In addition, specific algorithms will be developed to implement the methods on the computer. The general problem of robust system control consists of constructing fixed feedback controllers for possibly unstable families of systems with parameter or modelling uncertainty in order to stabilize the given family and in order to meet certain performance specifications. This proposal is concerned with an operator theoretic and functional analytic approach to this problem for multivariable, distributed, and even possibly nonlinear plants.

This project is mathematical research that has applications to the design of control systems. A variety of methods from functional analysis and operator theory will be brought to bear on problems involving matrix-valued analytic functions, in particular optimal supremum norm approximation by such functions and multivariable Nevanlinna - Pick interpolation problems. Results here are relevant to the computation of quantities which enable one to stabilize systems with parameter or modeling uncertainty while at the same time meeting certain performance specifications. Nonlinear as well as linear systems will be considered, with due attention to development of the underlying operator theory in the nonlinear case.

ECS-9700588 Tannenbaum The proposal deals with partial differential equation methods for the control of distributed and nonlinear systems. In particular, the focus is on the benchmark area of certain key semiconductor manufacturing processes including etching, deposition and lithography. We will also discuss some new directions we are taking on the robust control of distributed parameter systems using skew Toeplitz theory. This allows one to reduce the design of H -optimal and suboptimal compensators to finite dimensional linear algebra problem, the dimension of which only depends on the McMillan degrees of the weights and not the (state-space) dimension of the plant. Thus even for infinite dimensional systems, we are reduced to finite matrix manipulations. We will also consider some time-varying generalizations of these ideas.

IBN-9720305 PI: SHAPLEY This project is being funded through the Learning & Intelligent Systems Initiative. The questions involve vision and learning in the central nervous system. The project investigates how the brain represents and processes perceptual information, and the adaptive changes that occur when the system learns and improves its performance. Here the visual system is used as a gateway into the workings of the brain, employing methods from psychophysics, neurophysiology, mathematics and engineering. The work focuses on visual grouping, which is the ability of the visual system to link together local elements of the visual image into coherent wholes. Grouping is one of the most fundamental aspects of human vision, and the goal of this work is to obtain a theory of visual grouping that will explain the physiological and psychophysical data, and lead to new technological ideas to be applied in intelligent artificial systems. Results will be important because understanding the computations in the brain that produce grouping would be a leap forward in our understanding of brain function, and of any systems that can adapt to experience. This work will therefore have an impact in designing learning materials and in the optimal methods of presenting information, and in the design of the next generation of computer vision systems and intelligent control systems. This project is supported in part by the NSF Office of Multidisciplinary Activities in the Directorate for Mathematical & Physical Sciences.

Tannenbaum, Allen
ECS-0137412

The research program outlined in this proposal is driven by the need to develop novel means of acquiring, storing, manipulating and synthesizing signals and images for use in a feedback loop. This is the essential mandate of controlled active vision in which one uses a combination of techniques from systems and control, signal and image processing, as well as a computer vision for this purpose. The design of novel techniques for using visual information in control systems appears in a number of practical systems problems ranging from remote controlled weapons and vehicles to telesurgery, manufacturing systems, and ATR. Moreover, these efforts are leading to enhanced man-machine interfaces for interactions with computers.

In this research, the PI will consider certain novel methods based on the notion of "optimal mass transport" for such problems in controlled active vision. This type of technique has appeared in econometrics, fluid dynamics, transportation, statistical physics, shape optimization, expert systems, meteorology, and nonlinear control analysis and synthesis.

PI: Rina Tannenbaum NSF - SGER
PROJECT SUMMARY
One of the key issues in the assembly of printed circuit boards is the precise positioning of
the components and leads onto the metallic pads already present on the surface of the substrate. The
state of the art technology in this area involves the use of the stencil-printing process, in which a thin
layer of solder-paste is deposited on the surface of the substrate and pads, followed by the automatic
positioning of the components onto their designated places. The continued demand for higher component density of integrated circuits has lead to an ever-shrinking size of these components, and hence, the positioning issue has become the major handicap, due the very rigid requirements on the assembly process. In particular, the height, area or volume of solder-paste bricks may affect placement accuracy because of the lateral movement of components as leads move through the matrix in the placement process, thus reducing the yield and reliability of the high-density circuits. It is therefore expected that the current surface-mount technologies will soon reach their maximum capability to accommodate the growing needs of the industry and the shrinking size of the components, and as a consequence, component density would have reached saturation as well. To eliminate this bottleneck, a new surface-mount placement technology, operative in the nanometer (or sub-micron) size regime is sought. Hence, a new paradigm for the surface-mount placement process
will have to be implemented. At these sub-micron dimensions, the solder-paste technology will have
to be replaced by a smart, selective adhesive, that can essentially operate at the molecular-level,
and can selectively form precision molecular bridges between the nano-pads and the nanocomponents.
This proposal focuses on the utilization of well-known techniques from the surface selfassembly
field, in order to construct functional surfaces on the metallic nano-pads that will subsequently bind irreversibly and uniquely to the deposited nanocomponents with very low error and very few processing steps. The smart adhesive will comprise of molecules that will bind selectively to metallic surfaces, nanopads on one side and nanocomponents on the other, forming an interactive, bridging, conductive layer. The desired precision of the processes involved will also call for new ideas in feedback control. Measurements and evaluations of events at the molecular and nanoscale level will need to be translated into observable macroscopic quantities. Hence, mathematical models and resulting computer simulations of the type for which control/systems engineers have a particular expertise may be very helpful in driving some of the specific experiments. In particular, concepts of from particle systems and discrete Markov chains to model the processes involved may be useful. Therefore, the synergistic collaboration of a material scientist and a control theorist will constitute a great opportunity for a comprehensive nano-interconnect system
development.
The Intellectual Merit of the proposal lies in the bottom-up strategy for the design of an optimal system for a given application. Understanding, down to the molecular level, of the different requirements for the development of a surface-mount placement process that can successfully operate at the nanoscale regime, will afford the choice of the precisely correct building block for the synthesis and assembly of this system. The synergistic combination of experimental work and mathematical modeling will ensure that the process that will be developed will possess the optimal properties in terms of stability (chemical and thermal), selectivity and conductivity.
The Broader Impacts of the proposal are both technical and educational. On the technical side, the success of this work will no doubt constitute a paradigm shift in the field of surface mount technology, since it will open up a new size regime and new opportunities for component densities that were unattainable with existing technologies. Moreover, on the educational side, it will expose the graduate students working in these fields to a broader perspective of their area of research, and ultimately generate engineers who are comfortable and well educated in interdisciplinary environments.

B. PROJECT SUMMARY
In this research program, the PI proposes a novel combined geometric active contour/particle
filtering approach for tracking the boundaries of objects (i.e., planar shapes), when the observation
is an image which may be a complicated nonlinear function of the closed curve. The advantage
of using geometric active contours is that they allow topological changes (automatic merging and
breaking), and hence can be used to track multiple objects.
More specifically, the particle filtering framework will be applied to the space of continuous
closed curves which is an infinite dimensional space. This is a particularly difficult problem since
generating Monte Carlo samples from a very large dimensional (theoretically infinite) system noise
distribution is computationally complex. Moreover, the number of samples required for accurate
filtering increases with the dimension of the system noise. The PI will show that as long as the
number of dimensions of the system noise is small, even if the total state space dimension is
very large (or infinite), a particle filtering algorithm can be implemented which will allow him
to develop practical robust tracking algorithms. In particular, the PI proposes to approximate
curve deformation using a time- varying finite dimensional representation. He will formulate the
problem as particle filtering with unknown static parameters and use a modification of a particle
filter that has been shown to be asymptotically stable for tracking static parameters.
The main assumption is that even though the curve may be regarded as a point of an infinite
dimensional space, "most of its deformation" for a given period of time can be approximated using
a small finite number of dimensions. But over time, this approximation may no longer suffice
and hence one must allow the number of dimensions and the finite dimensional basis to change
whenever the current approximation is unable to track with suffcient accuracy. For a number
of key scenarios, this assumption seems reasonable, and allows the use of infinite dimensional
observer techniques for visual tracking.
Intellectual Merit:
The key objective of this project is the development of new methodologies for employing visual
information in a feedback loop, the underlying problem of controlled active vision. This is a
challenging problem both from the intellectual and practical points of view. Indeed, controlled
active vision, and in particular visual tracking requires the integration of techniques from control
theory, signal processing, and computer vision. This research program points the way to finding a
new class of robust and hopefully real-time visual tracking schemes making use of all of the above
building blocks.
Broader Impact of Research Activity:
The PI believes that the proposed synergy of vision, filtering, and control described in this
proposal may have a strong impact on tracking and active vision. Indeed, visual tracking provides
a fundamental example of the need for controlled active vision. While tracking in the presence of a
disturbance is a classical control problem, visual tracking raises new issues. Firstly, since cameras
are part of the system, one must consider the nature of the disturbance from imaging sensors.
Secondly, the feedback signal may require some interpretation of the image, e.g., segmentation
of a target from its background, or an inference about an occluder. Finally, as visual processing
becomes more complex, the issue of processing time arises. Each of these problems must be
answered before target detection, and visually-mediated control can be provided for medical,
commercial, or advanced weapon systems.

Blind source separation (BSS) refers to the task of identifying sources from their linear mixtures.
Traditional approaches to BSS have been limited to static mixtures. Furthermore, such approaches typically rely upon hard-to-exploit and non-robust assumptions on source-statistics. In contrast, the proposed research addresses the general problem of separating dynamically-mixed signals by simultaneously identifying both the dynamics as well as the input sources. The basic tool in the formulation of relevant ill-posed system identification problems is the notion of sparsity which is used as a regularization term to limit the choices of input/process dynamics in a natural way. The proposed research stands to benefit from a rather powerful theory on computationally-tractable sparsity-inducing optimization, based on ℓ1-functionals, which has taken shape in recent years.

The proposed plan begins with an analysis of a general dynamic-mixtures-model, exploring
sparsity as a regularizing term. Motivation for such models stems from system identification, distributed sensing, as well as problems in spectral analysis, subspace identification, and antenna arrays. The proposal continues on with an outline of specialized formalisms intent on capturing, in a similar framework, problems of delay/coherence analysis as well as of system identification in a non-stationary/nonlinear-mixing setting. To this end, it is proposed that the notion of joint sparsity?a form of dependent-component-analysis, is a suitable tool for identifying commonalities between sources, harmonics, etc., while seeking tell-tale signs of the presence of time-delays and of nonlinear mixing. The proposal covers in some detail the case of autoregressive dynamics which leads to a convex optimization problem. Tradeoffs between noise, model order, and stability are raised and integrated into the proposed research plans. Connections between BSS and image segmentation techniques?a form of geometric BSS, are highlighted in a way which suggests another conceptual angle for the proposed research. Finally, the issue of dictionary design is being discussed, i.e., how to obtain a suitable ?over-complete? basis for source signals and possibly system dynamics as well, based on prior information and on available data, in a way that will ensure a degree of robustness and computability while promoting sparsity.

Intellectual Merit: Practical as well as theoretical questions will be investigated with regard to the rather ubiquitous identification problem for system dynamics and signal transmission paths, in the presence of unknown disturbances and inputs. The formalism is cast in the context of blind source separation, and the basic new tool is the concept of sparsity with respect to suitably chosen collection of signals as a selection rule for modeling. The approach stands to benefit from the theory of sparse representations/compressive sensing which has come to fruition in recent years. Problems of delay estimation, coherence analysis, non-linear and non-stationary modeling are presented with a new angle?seeking relevant information in a jointly-sparse representation of measured time-series. A potentially transformative broad spectrum of tools may result from the new ways of analysis and system identification proposed herein.

Broader Impact: The research may impact very different fields such as Physics?in calibrating and filtering measurements, Image analysis?in MRI/medical imaging, System identification, Acoustics and the control of jitter, Communications?blind deconvolution in noisy and resonant channels, Radar processing, and others.

We are proposing a novel approach to diagnosing early Alzheimer?s disease (AD) and predicting progression via a robust biomarker that captures ?glymphatic? pathway transport on a systems level. The glymphatic pathway is a brain-wide system, which was recently discovered to function as a clearance pathway for toxic brain waste proteins including soluble amyloid beta (A?) and tau similarly to the classical body-wide lymphatic system. As such, the glymphatic pathway comprises a previously overlooked and unique compartment of the brain vasculature, the peri-vascular space wherein cerebrospinal fluid (CSF) is flowing and streaming into the brain interstitial fluid (ISF) space thereby forcing waste solutes out of the brain. Except for rare familial AD, where excessive A? production and deposition in the brain clearly drives cognitive decline, there is limited evidence in the more common sporadic AD that cerebral A? accumulation is the result of A??overproduction. In fact, emerging evidence suggests that parenchymal A? accumulation in sporadic AD is driven by reduced A? clearance. The glymphatic pathway is thus a prime candidate for linking disruptive clearance of A? to AD, and we will use this opportunity to develop new tools and computational analysis aimed explicitly at capturing global glymphatic pathway function and serve as a novel diagnostic AD biomarker. Currently there is no method available to capture all of the intricate and dynamic components of glymphatic transport, in particular, parenchymal transport and clearance pathways. We propose to integrate imaging techniques and develop novel computational analysis including optimal mass transport to characterize the glymphatic pathway as a brain-wide dynamic ?unit?. The ultimate goal of the proposed investigation is to apply the glymphatic biomarker and track its disruption in progressing vascular and parenchymal amyloid pathologies. The proposed studies are based on novel preliminary findings that 1) glymphatic transport can be visualized as an integrative system through perivascular and interstitial spaces; 2) that state dependent changes induced by specific anesthetic regimens which dramatically affect the glymphatic transport can be captured by optimal mass transport analysis; and 3) a new transgenic rat model of cerebral amyloid angiopathy (rTg-SwDI) which will be used for specific hypothesis testing against the transgenic rat AD model (rTgF344-AD36) in the proposed studies. The specific aims are the following: (1) To develop biomarkers to visualize and functionally quantify macroscopic, glymphatic transport based on computational analysis of MRI and macroscopic optical imaging of CSF tracers in normal young (3 month old) rats and (2) to determine how and when normal aging and specific AD-like cerebral vascular and parenchymal amyloid pathologies influence glymphatic transport in the brain using the computational pipeline developed in SA1. Successful completion of the proposed highly innovative experiments will yield an entirely new and promising biomarker to track reduced Aß clearance via the glymphatic pathway which is key to the propagation of CAA and AD.