Preface 1. Introduction Overview A Brief History of LMIs in Control Theory Notes on the Style of the Book Origin of the Book 2. Some Standard Problems Involving LMIs. Linear Matrix Inequalities Some Standard Problems Ellipsoid Algorithm Interior-Point Methods Strict and Nonstrict LMIs Miscellaneous Results on Matrix Inequalities Some LMI Problems with Analytic Solutions 3. Some Matrix Problems. Minimizing Condition Number by Scaling Minimizing Condition Number of a Positive-Definite Matrix Minimizing Norm by Scaling Rescaling a Matrix Positive-Definite Matrix Completion Problems Quadratic Approximation of a Polytopic Norm Ellipsoidal Approximation 4. Linear Differential Inclusions. Differential Inclusions Some Specific LDIs Nonlinear System Analysis via LDIs 5. Analysis of LDIs: State Properties. Quadratic Stability Invariant Ellipsoids 6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties State-to-Output Properties Input-to-Output Properties 7. State-Feedback Synthesis for LDIs. Static State-Feedback Controllers State Properties Input-to-State Properties State-to-Output Properties Input-to-Output Properties Observer-Based Controllers for Nonlinear Systems 8. Lure and Multiplier Methods. Analysis of Lure Systems Integral Quadratic Constraints Multipliers for Systems with Unknown Parameters 9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise State-Feedback Synthesis 10. Miscellaneous Problems. Optimization over an Affine Family of Linear Systems Analysis of Systems with LTI Perturbations Positive Orthant Stabilizability Linear Systems with Delays Interpolation Problems The Inverse Problem of Optimal Control System Realization Problems Multi-Criterion LQG Nonconvex Multi-Criterion Quadratic Problems Notation List of Acronyms Bibliography Index.

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Linear Matrix Inequalities in System and Control Theory

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.

Pattern Recognition and Machine Learning

Algorithms that must deal with complicated global functions of many variables often exploit the manner in which the given functions factor as a product of "local" functions, each of which depends on a subset of the variables. Such a factorization can be visualized with a bipartite graph that we call a factor graph, In this tutorial paper, we present a generic message-passing algorithm, the sum-product algorithm, that operates in a factor graph. Following a single, simple computational rule, the sum-product algorithm computes-either exactly or approximately-various marginal functions derived from the global function. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can be derived as specific instances of the sum-product algorithm, including the forward/backward algorithm, the Viterbi algorithm, the iterative "turbo" decoding algorithm, Pearl's (1988) belief propagation algorithm for Bayesian networks, the Kalman filter, and certain fast Fourier transform (FFT) algorithms.

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Factor graphs and the sum-product algorithm

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.

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Sequential Monte Carlo methods in practice

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.

Planning Algorithms: Introductory Material

Standard balanced-truncation or Hankel-norm model approximation methods are applied to augmentations of the controller which emerge when characterizing the class of all stabilizing controllers in terms of an arbitrary proper stable transfer function. In the method, scaling parameters are at the disposal of the engineer to achieve an appropriate compromise between preserving performance for the nominal plant and a certain type of robustness of plant variations. There are a number of unique features of the approach. One feature is that a straightforward reoptimization of a reduced-order controller is possible within the framework of the method. A second feature is that for controllers designed for simultaneous stabilization of a number of plants, the method seeks to preserve the performance/robustness of the reduced-order controller for each plant. >

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Controller reduction methods maintaining performance and robustness

A quasi-separation theorem for LQG optimal control with IQ constraints

This work is concerned with least-mean-squares (LMS) algorithms in continuous time for tracking a time-varying parameter process. A distinctive feature is that the true parameter process is changing at a fast pace driven by a finite-state Markov chain. The states of the Markov chain are divisible into a number of groups. Within each group, the transitions take place rapidly; among different groups, the transitions are infrequent. Introducing a small parameter into the generator of the Markov chain leads to a two-time-scale formulation. The tracking objective is difficult to achieve. Nevertheless, a limit result is derived yielding algorithms for limit systems. Moreover, the rates of variation of the tracking error sequence are analyzed. Under simple conditions, it is shown that a scaled sequence of the tracking errors converges weakly to a switching diffusion. In addition, a numerical example is provided and an adaptive step-size algorithm developed.

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Continuous-time tracking algorithms involving two-time-scale Markov chains

A key problem in robotics is the estimation of the location and orientation of objects from surface measurement data. This is termed pose estimation. A fundamental task is the pose estimation of known quadratic surfaces from, possibly noisy, data. A solution for this task facilitates pose estimation for more complex objects. Current algorithms frequently converge to local minima of the performance index and/or pay a high computing cost and/or are sensitive to noise, that are unsuited for online applications because of the intensive computer effort required. The goal is to develop a fast and robust algorithm for pose estimation using range data. Here, pose estimation is carried out using algebraic techniques in a two stage optimization procedure involving least squares estimation, or better the method of instrumental variables, and 3/spl times/3 matrix diagonalizations. The procedure leads to zero pose estimation error in the noise free finite data case, and in the case of infinite data with additive white noise.

John B. Moore

Papers

Controller reduction methods maintaining performance and robustness

A quasi-separation theorem for LQG optimal control with IQ constraints

Continuous-time tracking algorithms involving two-time-scale Markov chains

Pose estimation of quadratic surface using surface fitting technique

Finite-dimensional optimal controllers for nonlinear plants