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 paper deals with the design of Excitation and Measurement Patterns (EMP) for the identification of a class of dynamical networks whose topology has the structure of a Directed Acyclic Graph (DAG). In addition to the by now well known condition that the identifiabiltiy of any dynamical network requires that the sources be excited, the sinks be measured, and all other nodes be either excited or measured, we show that for DAGs two other types of nodes have special excitation and measurement requirements. Armed with this result, we propose a systematic procedure for the design of EMPs that guarantees identifiability of a network with DAG topology.

Excitation and Measurement Patterns for the Identifiability of Directed Acyclic Graphs

Discrete-Time Fake Riccati Equations for Kalman Filtering and Receding-Horizon Control

Sensitivity and Roundoff Noise Optimization of a State-Estimate Feedback Controller

The term `base flow' means the contribution of the aquifer flow which sustains the river flow during droughts and permits pumping activities the year round. This paper proposes a way to obtain rather rapidly a good approximation of the behaviour of the base flow of a watershed only after a few months of measurements. After some considerations about data collecting, the hydrological assumptions which have lead to a simple base flow model are explained. The mathematical procedure of identification of the parameters of the model is then described and applied to three subbasins of the Dyle basin.

An approach to follow the variation of the base flow of small watersheds

Ways in which advanced search methodologies from artificial intelligence and integer programming can contribute to solve the identification problem are investigated. Several such methods are reviewed, along with techniques that are introduced to increase their efficiency. It is shown that identification exercises can effectively be based on variants of the branch-and-bound procedure and that only an easily computable admissible heuristic evaluation function is missing for one to have a true A* procedure. The major innovation introduced is that a quick exploration of the state space can be made by mapping it at equidistant model structures by adding or deleting many more than one parameter at a time. This method, combined with the use of statistical tests, gives valuable information on subsets in which the best model structure should be searched for and also saves considerable computer time. Once a smaller subset that most probably contains the best model has been identified, it can be mapped in turn at a lower scale and so on until a solution has been found. The typical performances of the branch-and-bound procedure are illustrated on both simulated and industrial data. >

http://ieeexplore.ieee.org/iel5/164/5238/00203376.pdf

Michel Gevers

Papers

Excitation and Measurement Patterns for the Identifiability of Directed Acyclic Graphs

Discrete-Time Fake Riccati Equations for Kalman Filtering and Receding-Horizon Control

Sensitivity and Roundoff Noise Optimization of a State-Estimate Feedback Controller

An approach to follow the variation of the base flow of small watersheds

On the use of search methodologies in system identification