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

In this paper camera parameters are assumed to be known and a novel approach for essential matrix estimation is presented. We estimate the essential matrix from point correspondences between a stereo image pair. The technical approach we take is a generalization of the classical Newton method. It is well-known that the set of essential matrices forms a smooth manifold. Moreover, it is quite natural to minimise a suitable cost function the global minimum of which is the essential matrix we are looking for. In this paper we present several algorithms generalising the classical Newton method in the sense that (i) one of our methods can be considered as an intrinsic Newton method operating on the Riemannian manifold consisting of all essential matrices, (ii) the other two methods approximating the first one but being more efficient from a numerical point of view. To understand the algorithm requires a careful analysis of the underlying geometry of the problem.

Essential Matrix Estimation via Newton-type Methods

Minimum Variance Control Harnessed for Non-Minimum-Phase Plants

Stochastic adaptive estimation and control algorithms involving recursive prediction estimates have guaranteed convergence rates when the noise is not ‘too’ coloured, as when a positive-real condition on the noise mode is satisfied. Moreover, the whiter the noise environment the more robust are the algorithms. This paper shows that for linear regression signal models, the suitable introduction of while noise into the estimation algorithm can make it more robust without compromising on convergence rates. Indeed, there are guaranteed attractive convergence rates independent of the process noise colour. No positive-real condition is imposed on the noise model.

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Robust recursive identification of multidimensional linear regression models

SUMMARY In this paper we propose for scalar plants an adaptive LQG controller with adaptive input sensitivity function/loop transfer recovery of an associated adaptive LQ design. The sensitivity recovery can be viewed as a frequency-shaped loop recovery where the weights involve a sensitivity function. The adaptive loop/sensitivity recovery is achieved by feeding back the estimation residuals to the control through a stable bounded input, bounded output (BIBO) adaptive filter Q~. For simplicity we consider fixed but uncertain plants in the model set and identification schemes where there are consistent parameter estimates. For non-minimum phase plants an asymptotic partial recovery is achieved via a recursive least squares update of the BIBO filter Qk. The degree of recovery can be prescribed a priori between zero and the maximum possible. For the case of minimum phase plant estimates, full loop recovery may be achieved asymptotically by prescribing a maximum degree of recovery. The motivation for proposing the new adaptive control algorithm is to enhance robustness of adaptive LQG designs, taking advantage of the robustness enhancement properties of sensitivity/loop recovery for off-line designs. The robustness properties of the new algorithm are demonstrated by simulation results.

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John B. Moore

Papers

Essential Matrix Estimation via Newton-type Methods

Minimum Variance Control Harnessed for Non-Minimum-Phase Plants

Robust recursive identification of multidimensional linear regression models

Adaptive lqg controller with loop transfer recovery

On strong consistency of least squares identification algorithms