Tamer Basar

Bio: Tamer Basar is an academic researcher from University of Illinois at Urbana–Champaign. The author has contributed to research in topics: Nonlinear system & Amplifier. The author has an hindex of 11, co-authored 15 publications receiving 16287 citations.

A New Approach to Linear Filtering and Prediction Problems

Abstract: The clssical filleting and prediclion problem is re-examined using the Bode-Shannon representation of random processes and the ?stat-tran-sition? method of analysis of dynamic systems. New result are: (1) The formulation and Methods of solution of the problm apply, without modification to stationary and nonstationary stalistics end to growing-memory and infinile -memory filters. (2) A nonlinear difference (or differential) equalion is dericed for the covariance matrix of the optimal estimalion error. From the solution of this equation the coefficients of the difference, (or differential) equation of the optimal linear filter are obtained without further caleulations. (3) Tke fillering problem is shoum to be the dual of the nois-free regulator problem. The new method developed here, is applied to do well-known problems, confirming and extending, earlier results. The discussion is largely, self-contatained, and proceeds from first principles; basic concepts of the theory of random processes are reviewed in the Appendix.

Analysis of Recursive Stochastic Algorithms

Abstract: Recursive algorithms where random observations enter are studied in a fairly general framework. An important feature is that the observations may depend on previous ?outputs? of the algorithm. The considered class of algorithms contains, e.g., stochastic approximation algorithms, recursive identification algorithms, and algorithms for adaptive control of linear systems. It is shown how a deterministic differential equation can be associated with the algorithm. Problems like convergence with probality one, possible convergence points and asymptotic behavior of the algorithm can all be studied in terms of this differential equation. Theorems stating the precise relationships between the differential equation and the algorithm are given as well as examples of applications of the results to problems in identification and adaptive control.

Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Seminorms, and Approximate Inverses

Abstract: In this paper, the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization. Stable feedback schemes obtainable from a given plant are parameterized. Salient properties of sensitivity reducing schemes are derived, and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity. The theory is developed for input-output systems in a general setting of Banach algebras, and then specialized to a class of multivariable, time-invariant systems characterized by n × n matrices of H? frequency response functions, either with or without zeros in the right half-plane. The approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity, and on the concept of an approximate inverse. Approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction. An indicator of approximate invertibility, called a measure of singularity, is introduced. The measure of singularity of a linear time-invariant plant is shown to be determined by the location of its right half-plane zeros. In the absence of plant uncertainty, the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure. In particular, if there are no right half-plane zeros, sensitivity can be made arbitrarily small. The feedback schemes used in the optimization of sensitiviiy resemble the lead-lag networks of classical control design. Some of their properties, and methods of constructing them in special cases are presented.

Absolute Stability of Nonlinear Systems of Automatic Control

Abstract: The problem of absolute stability of an ?indirect control? system with a single nonlineartiy ia investlgated by using a method which differs from the second method of Lyapunov. The main condition of the obtained criterion of absolute stability is expressed in terms of the transfer function of the system linear part. It is also shown that by fonning the standard Lyapunov function -?a quadratic form plus the integral of the nonlinearity? It is not possible In the case considered here to obtain a wider stability domain than the one obtained from the presented criterion. Graphical criteria of absolute continuinty are also given by means of the phase-amplitude characteristic or by what is known as ?the modified phase-amplitude characteristic? of the system linear part.

Stabilized Feedback Amplifiers

Abstract: This paper describes and explains the theory of the feedback principle and then demonstrates how stability of amplification and reduction of modulation products, as well as certain other advantages, follow when stabilized feedback is applied to an amplifier. The underlying principle of design by means of which singing ia avoided is next set forth. The paper concludes with some examples of results obtained on amplifiers which have been built employing this new principle. The carrier-in-cable system dealt with in a companion paper1 involves many amplifiers in tandem with many telephone channels passing through each amplifier and constitutes, therefore, an ideal field for application of this feedback principle. A field trial of this system was made at Morristown, New Jersey, in which seventy of these amplifiers were operated in tandem. The results of this trial were highly satisfactory and demonstrated conclusively the correctness of the theory and the practicability of its commercial application.

Pattern Recognition and Machine Learning

Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Fundamentals of digital image processing

Abstract: Introduction. 1. Two Dimensional Systems and Mathematical Preliminaries. 2. Image Perception. 3. Image Sampling and Quantization. 4. Image Transforms. 5. Image Representation by Stochastic Models. 6. Image Enhancement. 7. Image Filtering and Restoration. 8. Image Analysis and Computer Vision. 9. Image Reconstruction From Projections. 10. Image Data Compression.

Sequential Monte Carlo methods in practice

Abstract: Monte Carlo methods are revolutionizing the on-line analysis of data in fields as diverse as financial modeling, target tracking and computer vision. These methods, appearing under the names of bootstrap filters, condensation, optimal Monte Carlo filters, particle filters and survival of the fittest, have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques, including convergence results and applications to tracking, guidance, automated target recognition, aircraft navigation, robot navigation, econometrics, financial modeling, neural networks, optimal control, optimal filtering, communications, reinforcement learning, signal enhancement, model averaging and selection, computer vision, semiconductor design, population biology, dynamic Bayesian networks, and time series analysis. This will be of great value to students, researchers and practitioners, who have some basic knowledge of probability. Arnaud Doucet received the Ph. D. degree from the University of Paris-XI Orsay in 1997. From 1998 to 2000, he conducted research at the Signal Processing Group of Cambridge University, UK. He is currently an assistant professor at the Department of Electrical Engineering of Melbourne University, Australia. His research interests include Bayesian statistics, dynamic models and Monte Carlo methods. Nando de Freitas obtained a Ph.D. degree in information engineering from Cambridge University in 1999. He is presently a research associate with the artificial intelligence group of the University of California at Berkeley. His main research interests are in Bayesian statistics and the application of on-line and batch Monte Carlo methods to machine learning. Neil Gordon obtained a Ph.D. in Statistics from Imperial College, University of London in 1993. He is with the Pattern and Information Processing group at the Defence Evaluation and Research Agency in the United Kingdom. His research interests are in time series, statistical data analysis, and pattern recognition with a particular emphasis on target tracking and missile guidance.

Planning Algorithms: Introductory Material

Abstract: Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.