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

This short paper studies a particular class of optimization problems dealing with the selection, at each instant of time, of one out of many actuators in order to obtain a determined result. A cost is associated with each actuator. The cost function is the integral of a weighted combination of the achieved accuracy on the state of the system and the control energy. The control energy term depends upon both the selected actuator and the magnitude of the applied control. The problem is to design an optimal actuator selection strategy. The analysis is limited to the class of linear deterministic systems with measurable states. A discrete approach is considered. The analytic solution to this optimization problem is given first. When the number of actuators and the number of stages in the time interval become large the optimal analytic solution requires a considerable combinatorial work; a suboptimal algorithm is then proposed to alleviate this defect.

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On optimal and suboptimal actuator selection strategies

A new robust control design procedure based on a PE identification uncertainty set

Adaptive Control of the Temperature of a Glass Furnace

Introducing Caution in Iterative Controller Design

In this paper, a first step is taken to avoid ill-conditioning in adaptive estimation and pole assignment schemes for the case when there is a signal model overparametrization. Such a situation can occur in practice when an unknown model order is guessed too high so as to be on the "safe" side. The methods proposed in the paper are relatively simple compared to on-line order determination, being based on introducing suitable excitation in the "regression" vectors of the parameter estimation algorithms to ensure parameter convergence. For the case when the models are nonunique in that pole-zero cancellations can occur,the algorithms seek to estimate the unique model where the cancellations occur at the origin. Applying estimates of this (unique) model turns out to avoid ill-conditioning in central tendency adaptive pole assignment. For the case of one pole-zero cancellation the convergence theory of the algorithm is complete. For the more general case, algorithms are readily devised which appear to work well but for which a complete theory is not available.

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Michel Gevers

Papers

On optimal and suboptimal actuator selection strategies

A new robust control design procedure based on a PE identification uncertainty set

Adaptive Control of the Temperature of a Glass Furnace

Introducing Caution in Iterative Controller Design

On adaptive estimation and pole assignment of overparametrized systems