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

We develop an interior-point technique for solving quadratic programming problem in a Hilbert space. As an example we consider an application of these results to the linear-quadratic control problem with linear inequality constraints. It is shown that the Newton step in this situation is basically reduced to solving the standard linear-quadratic control problem.

http://ieeexplore.ieee.org/iel2/3470/10221/00480239.pdf

Long step path-following algorithm for the convex quadratic programming in a Hilbert space

Consideration is given to the requirements of a water waveform recording instrument and to the details of an instrument designed to meet these requirements. The instrument has a linear calibration, and tests show that over a wide range of conditions its accuracy is to better than 2%. A capacitance type sensing element is used, together with transistor circuits and a pen recorder. The device is suitable for recording water waves in hydraulic models.

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A water wave recording instrument for use in hydraulic models

This paper presents an application of adaptive control to flutter suppression for an aircraft flying in turbulence. The adaptive control law is integrated with a nominal constant gain controller and furnishes the equivalent of a 180° phase margin at the flutter frequency. The design approach blends the classical, linear quadratic Gaussian and adaptive synthesis techniques so that each contributes at its point of strength to achieve a robust control law with good performance characteristics. It is shown that the adaptive controller stabilizes the flutter in the face of arbitrary initial parameter estimates, unmodeled stochastic inputs and significant level of spillover dynamics. The results presented in this paper are very encouraging and motivates continuing work in the field.

Adaptive Flutter Suppression in the Presence of Turbulence

In this paper, we consider a path following algorithm for
 solving infinite quadratic programming problems.
 The convergence properties of a smoothly parametrized curve,
 known as the central trajectory, is studied. We show that
 the points of this curve converge to the optimal solution of
 the problem, so by approximating this curve, solutions
 arbitrarily close to the optimal solution can be calculated.
 As an example, we consider the linear-quadratic optimal
 control problem with state inequality constraints at
 every time instant.

http://users.rsise.anu.edu.au/~john/papers/JOUR/164.PDF

A path following algorithm for infinite quadratic programming on a Hilbert space

This paper considers the solution of a Fredholm equation occurring in detection theory problems. A solution procedure, based on solving differential equations with nonmixed boundary conditions, is described for the case when the kernel of the integral equation is known to be the output covariance of a linear finite-dimensional system excited by white noise. Solutions with discontinuities are considered.

John B. Moore

Papers

Long step path-following algorithm for the convex quadratic programming in a Hilbert space

A water wave recording instrument for use in hydraulic models

Adaptive Flutter Suppression in the Presence of Turbulence

A path following algorithm for infinite quadratic programming on a Hilbert space

Study of an integral equation arising in detection theory