Non-Model Based Intelligent Control of Engineering Systems

Organizers:
Warren Dixon (University of Florida, Gainesville, USA)

Additional Participants:
Miroslav Krstic ( University of California San Diego, USA)
Frank L. Lewis (University of Texas Arlington, USA)
Kevin L. Moore (Colorado School of Mines, USA)

Abstract:The purpose of this workshop is to present a detailed examination of four non-model based intelligent control methods including: iterative learning control, extremum seeking control, fuzzy and neural network control, and RISE control. The presenters will provide a historical perspective and motivation for each method.

The advantages of each method will be described along with underlying assumptions and constraints to help motivate the appropriate applicative context for each method. The fundamental principles of each method will be described with progressive development to advanced topics. Each section concludes with a discussion of example applications, experimental results, open technical problems, and future research directions.

The desired outcome of the workshop is to provide a detailed exposition of the methods such that the audience appreciates the advantages and limitations of the various methods for different classes of practical engineering applications.

Workshop URL:

(Top)

Identification of Hybrid Models via Generalized Principal Component Analysis

Organizers:
Rene Vidal (Johns Hopkins University, USA)
Yi Ma (University of Illinois, Urbana-Champaign, USA)

Additional Participants:

Summary: Over the past two decades, we have seen tremendous advances on the simultaneous segmentation and estimation of a collection of models from sample data points, without knowing which points correspond to which model. These advances have been motivated and constantly driven by numerous potential applications in hybrid system identification, computer vision, image processing, systems theory, robotics, and more recently, also in biological systems.

Most existing hybrid model identification methods treat the data segmentation problem as "chicken-and-egg problem". This is because in order to estimate a mixture of models one needs to first segment the data. Conversely, in order to segment the data one needs to know the model parameters. Therefore, data segmentation is usually solved in two stages (1) data clustering and (2) model fitting, or else iteratively using, e.g. the Expectation Maximization (EM) algorithm.

This tutorial will show that for a wide variety of hybrid model identification problems (e.g. mixtures of subspaces, mixtures of rigid-body motions, mixtures of linear dynamical models), the "chicken-and-egg" dilemma can be tackled using an algebraic geometric technique called Generalized Principal Component Analysis (GPCA). The main idea behind GPCA is to eliminate the data segmentation step algebraically and then use all the data to recover all the models without previously segmenting the data as follows:

1. Fit a set of polynomials to all data points, without clustering the data

2. Obtain the model parameters for each group from the derivatives of these polynomials.


The workshop will include several applications of GPCA to hybrid system identification and computer vision problems such as image/video segmentation, 3-D motion segmentation, and dynamic texture segmentation.

Workshop URL:

(Top)

Optimization On Manifolds

Organizers:
P.-A. Absil (Department of Mathematical Engineering, Universit´e Catholique de Louvain, Belgium)
Knut Huper (National ICT Australia)
Rodolphe Sepulchre (Department of Electrical Engineering and Computer Science, Universite de Liege, Belgium)

Additional Participants:
Uwe Helmke (University of Wurzburg, Germany)
Michel Journee (Universite de Liege, Belgium)
Shankar Sastry (University of California, Berkeley, USA)
Jochen Trumpf (Australian National University, Canberra, Australia)

Summary: The goal is to provide the participants with the background necessary to design and analyze optimization methods on manifolds and turn these methods into concrete numerical algorithms for several problems in control, computer vision and signal processing.

The recent years have witnessed an increasing interest in the development of efficient optimization algorithms defined on manifolds. Applications abound in numerical linear algebra (eigenproblems), statistical analysis (Principal and Independent Component analysis), signal processing (blind source separation, subspace tracking), machine learning (clustering), computer vision (pose estimation), to name a few. Good algorithms result from the combination of insights from differential geometry, optimization and numerical analysis.

The purpose of the workshop is to provide a tutorial introduction to this rich field of applied mathematics with a parsimonious selection of topics in differential geometry and in numerical algebra, and with an illustration of engineering problems where the theory is currently applied. Introductory talks provide the participants with the basic concepts of differential geometry instrumental to algorithmic development. The other talks illustrate why differential geometry provides a natural foundation for the development of efficient numerical algorithms for many equality-constrained optimization problems. Several well-known optimization techniques, such as steepest descent, conjugate gradients, trust-region and Newton-type methods, are generalized to the manifold setting. A generic development of each of these methods is provided, building upon the geometric material. The participants are then guided through the constructions and computations that turn these geometrically formulated methods into concrete numerical algorithms. The techniques are general and are illustrated on several problems in linear algebra, signal processing, data mining, computer vision, and statistical analysis.

Workshop URL:

(Top)

Identification of continuous-time models from sampled data

WITHDRAWN.

(Top)