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

This paper considers the problem of minimizing a quadratic cost subject to purely quadratic equality constraints. This problem is tackled by first relating it to a standard semidefinite programming problem. The approach taken leads to a dynamical systems analysis of semidefinite programming and the formulation of a gradient descent flow which can be used to solve semidefinite programming problems. Though the reformulation of the initial problem as a semidefinite pro- gramming problem does not in general lead directly to a solution of the original problem, the initial problem is solved by using a modified flow incorporating a penalty function.

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A Dynamical Systems Analysis of Semidefinite Programming with Application to Quadratic Optimization with Pure Quadratic Equality Constraints

If more than one pulse train is transmitted over the same communication channel, a challenge is to separate them for source identification at the receiver. This is known as pulse train deinterleaving, and is clearly a fundamental problem in the study of discrete-event systems. We present an approach for deinterleaving pulse trains and estimating their periods using an extended Kalman filter (EKF). A form of smoothing of the discontinuities is proposed so that the EKF approach becomes attractive. The advantage of this EKF approach is that it is less computationally expensive than most previously proposed methods. The method proposed appears to give useful results for up to seven or so pulse trains, particularly when there is some a priori information on the pulse frequencies, which can be obtained using computations of order Nlog N.

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The limits of extended Kalman filtering for pulse train deinterleaving

A Kalman filter with adaptive frequency-shaped gains, suitable for operating in unknown colored noise environments, is described. The scheme uses least-squares parameter updates and is inherently stable. The adaptive loop enhances the performance of the filter under adverse operating conditions but evanesces under nominal designed condition, thereby preserving the desirable properties of an offline design. Simulation results show that the scheme is effective in enhancing Kalman filter performance when applied to other than nominal signal models. >

Adaptive frequency shape Kalman filters

The `circle criteria? for giving stability information of linear systems containing one time-varying element are shown to have useful graphical interpretations for design purposes on a parameter-plane diagram. The significance of the parameter-plane approach is that, in a system design, the adjustable parameters of either the time-varying element or the time-invariant subsystem may be selected to satisfy the system stability constraints directly from the diagram. This means that for some design problems the parameter-plane approach is more efficient than the application of the well known complex-plane methods.

'Circle criteria' in the parameter plane

Pulse trains from a number of different sources are often received on the one communication channel. It is then of interest to identify which pulses are from which source, based on different source characteristics. This sorting task is termed dein- terleaving. In this paper we next propose time-domain techniques for deinterleaving pulse trains from a finite number of periodic sources based on the time of arrival (TOA) and pulse energy, if available, of the pulses received on the one communication channel. We formulate the pulse train deinterleaving problem as a stochastic discrete-time dynamic linear model (DLM), the "discrete-time" variable k being associated with the kth received pulse. The time-varying parameters of the DLM depend on the se- quence of active sources. The deinterleaving detectionlestimation task can then be done optimally via linear signal processing using the Kalman filter (or recursive least squares when the source periods are constant) and tree searching. The optimal solution, however, is computationally infeasible for other than small data lengths since the number of possible sequences grow exponentially with data length. Here we propose and study two of a number of possible suboptimal solutions: 1) Forward dynamic programming with fixed look-ahead rather than total look-ahead as required for the optimal scheme; 2) a probabilistic teacher Kalman filtering for the detection/estimation task. In simulation studies we show that when the number of sources is small, the proposed suboptimal schemes yield near-optimal estimates even in the presence of relatively large jitter noise. Also, issues of robustness and generalizations of the approach to the case of missing pulses, unknown source number, and non-Gaussian jitter noise are addressed.

http://ieeexplore.ieee.org/iel4/78/7823/00330369.pdf

John B. Moore

Papers

A Dynamical Systems Analysis of Semidefinite Programming with Application to Quadratic Optimization with Pure Quadratic Equality Constraints

The limits of extended Kalman filtering for pulse train deinterleaving

Adaptive frequency shape Kalman filters

'Circle criteria' in the parameter plane

Deinterleaving Pulse Trains Using Discrete-Time