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AIME@CZ 2012 Czech workshop on applied mathematics in engineering 7-8 November 2012 Charles Square Campus of the Czech Technical University in Prague, Czech Republic The Department of Control Engineering & The Center for Machine Perception FEE CTU in Prague |
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Wednesday 7 November 2012
Thursday 8 November 2012
| Vladimír Kučera (bio) | Polynomial Equation Approach to Linear Control System Design |
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Abstract: |
Polynomial techniques have made important contributions to systems and control theory. Engineers in industry often find polynomial and frequency domain methods easier to utilize than state equation based techniques. Control theorists show that results obtained in isolation using either approach are in fact closely related. Polynomial system description provides input-output models for linear systems with rational transfer functions. These models display two important system properties, namely poles and zeros, in a transparent manner. A performance specification in terms of polynomials is natural in many situations; see pole allocation techniques. A specific control system design technique, called polynomial equation approach, was developed in the 1960s and 1970s. The distinguishing feature of this technique is a reduction of controller synthesis to a solution of linear polynomial equations of specific (Diophantine or Bézout) type. In most cases, control systems are designed to be stable and to meet additional specifications, such as optimality and robustness. It is therefore natural to design the systems step by step: stabilization first, then the additional specifications each at a time. For this it is obviously necessary to have any and all solutions of the current step available before proceeding any further. This motivates the need for a parametrization of all controllers that stabilize a given plant. In fact this result has become a key tool for the sequential design paradigm. The additional specifications are met by selecting an appropriate parameter. This is simple, systematic, and transparent. However, the strategy suffers from an excessive grow of the controller order. This plenary is a guided tour through the polynomial control system design. The origins of the parametrization of stabilizing controllers, called Youla-Kučera parametrization, are explained. Historical and personal notes are added. Standard results on pole placement and H2 control are summarized. New and exciting applications of the parametrization result are then discussed: stabilization subject to input constraints, output overshoot reduction, fixed order controller design, and robust stabilization. |
| Jan Flusser (bio) | The beauty of deconvolution. |
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Abstract: |
This talk is devoted to deconvolution problem in image processing, namely to its ill-posed and ill-conditioned formulation. We present a unified approach to this problem based on a regularized minimization of a proper energy functional. After the explanation of mathematical background, several applications including embedded solution in smartphones will be demonstrated. |
| Josef Málek (bio) | Implicitly constituted fluids and solids: modeling, analysis and computation |
| Abstract | Implicit constitutive theory that is based on the idea of expressing the response of bodies by an implicit relation between the stress and appropriate kinematical variables, is capable of describing some of the material properties that explicit models seem unable to describe. It also provides a less standard interesting structure of the governing equations. After introducing implicit constitutive relations to describe the response of both non-linear fluids and solids, we will present several examples emphasizing the advantages of this framework on three levels: modeling of material responses, theoretical analysis of related boundary values problems and computer simulations. |
| Fredrik Kahl (bio) | Efficient and Robust Optimization Techniques in Computer Vision |
| Abstrakt | There have
been major advances in optimization techniques for
many problems in computer vision in the last decade.
In the first part of this talk, I will focus on
graph cuts which is by now a standard tool for
applications like image segmentation, stereo and
denoising. The method is capable of efficiently
computing optimal solutions for large-scale problems
with submodular cost functions. It can also be used
for approximating hard, non-submodular problems. New
results on how to construct the best lower-bounding
approximation, the so-called generalized roof dual,
will be presented. In particular, a polynomial-time
algorithm for computing a solution that attains the
bound will be described. In the second part, another standard tool namely RANSAC will be reviewed. It is one of the most successful approaches for handling the large amounts of outliers occurring in multiple view geometry and registration problems. The general goal of RANSAC is to find the solution which has the maximum number of inliers. However, the method has no guarantee of finding the optimal solution. I will show how one can modify the standard scheme and obtain such guarantees with a polynomial-time algorithm. Other goal functions, such as the truncated L2-norm, will also be considered. |
| Pavel Trnka | Distributed Optimization and Model Predictive Control |
| Abstract | Many large-scale optimization problems arising from practical applications can be effectively decomposed to multiple small problems and solved in coordinated iterations. The talk will introduce decomposition and coordination principles and analogies. Then it will target distribution methods for model predictive control, which is the most successful advanced control strategy used in the industry. Finally a fast coordination method based on a multi-parametric programming will be presented and demonstrated on distributed controller for Barcelona city water distribution network. |
| Zdeněk Strakoš (bio) | Challenges in coupling iterative algebraic computations with modeling and discretisation |
| Abstract | The
current state-of-the art of iterative solvers is the
outcome of the tremendous algorithmic development
over the last few decades and of investigations of
{\em how} to solve given problems. In this
contribution we focus on Krylov subspace methods and
more on the dual question {\em why} things do or
might not work in solving practical problems. This
requires considering the algebraic computations in
the context of the mathematical properties of the
underlying model and its discretisation, with the
tools ranging from functional analysis to
approximation and matrix theory. We will pose and discuss, in particular, open questions such as what does the spectral information tell us about the behaviour of Krylov subspace methods, to which extent we can relax the accuracy of local operations in {\em inexact} Krylov subspace methods without causing an unwanted delay, how important is considering rounding errors in various algorithmic techniques, whether it is useful to view Krylov subspace methods as {\em matching moment model reduction}, and how the algebraic error can be included into locally efficient and fully computable {a-posteriori} error bounds for adaptive PDE solvers. |
| Xavier Goaoc (bio) | From geometric optimization to nerve theorems ... and back |
| Abstract | This talk will explore some of the connections between a fundamental problem in computational geometry, the efficient computation of the cylinder best fitting a set of points, and classical questions in discrete geometry, line geometry and topological combinatorics: Helly numbers, geometric permutations, nerve theorems ... |
| Tomáš Werner (bio) | Marginal Equalization in Constraint Networks and Graphical Models over Commutative Semirings |
| Abstract | Constraint
propagation, or local consistency, is ubiquitous in
constraint satisfaction. Recently, techniques
similar to classical constraint propagation have
been developed that are applicable to soft versions
of constraint satisfaction problems. In computer
vision and machine learning, this kind of techiques
is known as message passing. We present a version of constraint propagation that applies to a wide class of generalized constraint satisfaction problems, defined in terms of commutative semirings. This constraint propagation consists in locally transforming the problem to an equivalent problem so that marginals of overlapping problems overlap. The technique is a generalization of the max-sum diffusion algorithm, proposed in 1976 by Schlesinger et al. |
| Lenka Zdeborová (bio) | Compressed sensing: How insight from statistical physics leads to optimality |
| Abstract | Compressed sensing is a revolutionary idea in signal acquisition, allowing to measure signals directly in their compressed form while being able to "decompress" without losses in a tractable way. Algorithms based on linear programming and L1 regularization were the state of the art for this task until recently. Our insight from statistical physics studies leads to an astonishing new compressed sensing scheme: Combining a belief-propagation-like algorithm with a special design of measurements allows to perform not only better than previously, but also to achieve asymptotically the information theoretically best possible performance. My aim is to review these results in a broadly accessible manner letting most of the details for a discussion. |
