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

An explicit connection is made between the (nonadaptive) control law design stage of predictive adaptive control and techniques of linear-quadratic-Gaussian control with loop transfer recovery for robustness enhancement. The inherent controller design robustness of these methods is examined in terms of the nonadaptive closed-loop properties, that is of the class of open-loop perturbations to which the closed-loop system is robust, and of the effected input spectrum to the plant in closed loop. With this latter information, the authors then pose the question of to which plant model does the recursive least squares identification stage converge under this input. It is found that in many circumstances the identified model is precisely that which yields the best satisfaction of the previous robustness criterion for the control law. In this way, the authors demonstrate the robust interplay of the identifier and the controller in this class of adaptive control methods. >

Adaptation and robustness in predictive control

A brief introduction is given to the problems of parametrization and identifiability. A distinction between identifiability of specific parameters and identifiability of a model structure is introduced. For the latter, the structure and some possible parametrizations are presented for the set of all linear multivariable systems of given McMillan degree.

Parametrization issues in system identification

In a recent paper (Gevers et al., CDC 2013) [6] we have presented identifiability and excitation conditions for a class of linearly parametrized polynomial systems with a scalar state. The present paper expands the model class in two ways: we consider a class of rational systems with vector states that can be written in the so-called “generalized controller form”. The identifiability for such systems can be determined using the Ritt algorithm as shown in the seminal paper (Ljung and Glad, 1994) [10]. Here we present an alternative and simple method which offers a lot of insight into the structural conditions on the model class that make it globally identifiable and into the generation of informative experiments.

Identifiability and excitation of a class of rational systems

We present conditions under which the persistency of excitation of one regressor vector implies the persistency of another regressor derived from the first via a linear, dynamical transformation.

Persistence of excitation criteria

In many practical cases, the identication of a system is done in closed loop with some controller. In this paper, we show that the internal stability of the resulting model, in closed loop with the same controller, is not always guaranteed if this controller is unstable and/or nonminimum phase, and that the classical closed-loop prediction-error identication methods present dieren t properties regarding this stability issue. With some of these methods, closed-loop instability of the identied model is actually guaranteed. This is a serious drawback if this model is to be used for the design of a new controller. We give guidelines to avoid the emergence of this instability problem; these guidelines concern both the experiment design and the choice of the identication method.

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Michel Gevers

Papers

Adaptation and robustness in predictive control

Parametrization issues in system identification

Identifiability and excitation of a class of rational systems

Persistence of excitation criteria

Closed-loop identication with an unstable or nonminimum phase controller