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

http://control.disp.uniroma2.it/galeani/CO/materiale/automatica2000.pdf

Survey Constrained model predictive control: Stability and optimality

A new approach is presented to the problem of detecting the number of signals in a multichannel time-series, based on the application of the information theoretic criteria for model selection introduced by Akaike (AIC) and by Schwartz and Rissanen (MDL). Unlike the conventional hypothesis testing based approach, the new approach does not requite any subjective threshold settings; the number of signals is obtained merely by minimizing the AIC or the MDL criteria. Simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented.

Detection of signals by information theoretic criteria

Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra. Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.

http://www.eeci-institute.eu/GSC2011/Photos-EECI/EECI-GSC-2011-M5/book_AMS.pdf

Optimization Algorithms on Matrix Manifolds

https://www.itk.ntnu.no/fag/fordypning/TK16-filer/Samling1_MorariLee.pdf

Model predictive control: past, present and future

We consider a class of single input single output second order nonlinear systems whose coefficients are bounded and have bounded time-variation. We describe an adaptive observer/identifier for these systems and derive sufficient conditions on the system and on the inputs that guarantee global stability of this adaptive observer. We present an application to a robot manipulator with two degrees of freedom.

A Stable Adaptive Observer for a Class of Nonlinear Second Order Systems

The accuracy of plant parameters estimated in closed-loop operation is investigated for a class of multivariable systems and for the situation where only some of the reference inputs are excited. This, issue is important for at least two reasons: (i) there are control applications where it is preferable not to excite all references in order to avoid performance degradation, and (ii) it is not clear whether the results in the context of open-loop identification. where the existence of common parameters between the various transfer functions is a condition for improved accuracy with additional excitation, also hold in the closed-loop case. The paper examines the effect of the non-excitation of some reference inputs on the variance of the estimated parameters. The proposed expressions are valid for all conventional model structures used in prediction error identification. Although exciting all reference inputs is not necessary for identifiability, this work shows that, regardless of the parametrization, the excitation of all references never worsens and, in most cases, improves the accuracy of the parameter estimates. The analytical results developed in this work are illustrated by two simulation examples. (C) 2008 Elsevier Ltd. All rights reserved.

Closed-loop identification of multivariable systems: With or without excitation of all references?

In our previous paper (1998), we compared model reduction, in both open and closed loops, with closed-loop identification of a low-order model. Both methods were applied to the design of a controller for the secondary circuit of a nuclear pressurized water reactor (PWR), leading to the conclusions that system identification is a viable alternative to model reduction, and that the key feature for a successful control design is not so much the choice between order reduction or identification, but between open-loop and closed-loop techniques. In the present paper, we go further in this study and we compare model reduction with controller reduction for the same PWR system. We show that closed-loop techniques are more powerful than open-loop ones, and that controller reduction gives better results than model reduction when appropriate frequency weighting are chosen.

http://ieeexplore.ieee.org/iel5/6713/17969/00833272.pdf

A comparison between model reduction and controller reduction: application to a PWR nuclear plant

Relating H 2 and H bounds for finite-dimensional systems

The Local Polynomial Method (LPM) is a recently developed procedure for nonparametric estimation of the Frequency Response Function (FRF) of a linear system Compared with other nonparametric FRF estimates based on windowing techniques, it has proved to be remarkably efficient in reducing the leakage errors caused by the application of Fourier transform techniques to non periodic data In this paper we propose a modification of the LPM that takes account explicitly of constraints between the coefficients of the polynomials at neighbouring frequencies This new variant contributes a new and significant reduction in the Mean Square Error of the FRF estimates We also discuss the effects of the various design parameters on the accuracy of the estimates

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Michel Gevers

Papers

A Stable Adaptive Observer for a Class of Nonlinear Second Order Systems

Closed-loop identification of multivariable systems: With or without excitation of all references?

A comparison between model reduction and controller reduction: application to a PWR nuclear plant

Relating H 2 and H bounds for finite-dimensional systems

The Local Polynomial Method for nonparametric system identification: Improvements and experimentation