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

Survey Constrained model predictive control: Stability and optimality

Linear Dynamical Systems.- Semigroups, Generators, and Resolvents.- Perturbation and Approximation of Semigroups.- Spectral Theory for Semigroups and Generators.- Asymptotics of Semigroups.- Semigroups Everywhere.- A Brief History of the Exponential Function.

https://www.springer.com/productFlyer_978-0-387-98463-6.pdf?SGWID=0-0-1297-1590487-0

One-Parameter Semigroups for Linear Evolution Equations

The description of coherent features of fluid flow is essential to our understanding of fluid-dynamical and transport processes. A method is introduced that is able to extract dynamic information from flow fields that are either generated by a (direct) numerical simulation or visualized/measured in a physical experiment. The extracted dynamic modes, which can be interpreted as a generalization of global stability modes, can be used to describe the underlying physical mechanisms captured in the data sequence or to project large-scale problems onto a dynamical system of significantly fewer degrees of freedom. The concentration on subdomains of the flow field where relevant dynamics is expected allows the dissection of a complex flow into regions of localized instability phenomena and further illustrates the flexibility of the method, as does the description of the dynamics within a spatial framework. Demonstrations of the method are presented consisting of a plane channel flow, flow over a two-dimensional cavity, wake flow behind a flexible membrane and a jet passing between two cylinders.

https://hal-polytechnique.archives-ouvertes.fr/hal-01020654/document

Dynamic mode decomposition of numerical and experimental data

1. Introduction. 2. Linear Algebra. 3. Linear Systems. 4. H2 and Ha Spaces. 5. Internal Stability. 6. Performance Specifications and Limitations. 7. Balanced Model Reduction. 8. Uncertainty and Robustness. 9. Linear Fractional Transformation. 10. m and m- Synthesis. 11. Controller Parameterization. 12. Algebraic Riccati Equations. 13. H2 Optimal Control. 14. Ha Control. 15. Controller Reduction. 16. Ha Loop Shaping. 17. Gap Metric and ...u- Gap Metric. 18. Miscellaneous Topics. Bibliography. Index.

/pdf/essentials-of-robust-control-3kaks6yk3h.pdf

Essentials of Robust Control

Time-delay systems: an overview of some recent advances and open problems

Global stability analysis of fluid flows is presented as a method of extracting physical eigenmodes with associated linear dynamic models. These reduced-order models (ROM) are optimal for the transients near the onset of instability. We describe the computational aspects of the eigenmode extraction in detail. This outline includes (i) the discretization technique of the eigenproblem in the framework of computational fluid dynamics (CFD) and (ii) the solution algorithms for the discretized eigenproblem. As regards physical aspects, the linear ROM are improved by enriching the basis with POD modes and by incorporating weakly nonlinear base flow variations. Results of stability computations are presented for the circular cylinder wake, the flow around a NACA-0012 airfoil and the optimization of passive control. Preliminary 3D eigensolutions show the potential of the global stability method.

Global Stability Analysis for Linear Dynamics

Available solutions to sampled-data H2 optimal control problems for systems with input delays begin with a conversion to a discrete-time problem with input delays, followed by a matching optimization method geared to handle delays. We propose to reverse that order and address the delay first, by an analog loop transformation. Hence, discretization and optimization involve no delays and are amenable to any standard method. The proposed, streamlined, approach fits also previously unsolved problems where sampling and / or hold functions are design parameters.

Analog loop shifting in H 2 optimization of input-delay sampled-data systems

This paper proposes a harmonic-like decomposition to represent periodic systems with drift in either the period itself or the inter-period behavior, or both. The system is decomposed into two factors: a memoryless system-meant to represent the instantaneous period-and a slowly time varying system-meant to represent any drift in the inter-period behavior. The factorization is appropriate for real-time applications since it allows for on-line period updating. A general structure for real-time identification based on the proposed decomposition is also discussed.

Periodic systems with drift. I. Modeling and identification

We present an efficient pipeline for the segmentation and tracking of the Epicardium (Epi) and Left Ventricle (LV) from a set of 3D cardiac MRI sequences. The surface structure is handled as an array of planar active contours, interconnected between adjacent slices and frames, providing spatial and temporal consistency. In a given cardiac phase, the stacking of slice contours constitute a 3D mesh with a cylindrical topology. In a first stage the heart region is automatically localized by making use of the time variance of the heart region. Extraction of heart border is performed by means of energy minimization. Finally, we construct a 3D tensor array from all time surfaces in cylindrical coordinates and time and space consistency of the segmentation is enforced by fitting an m-variate tensor smoothing spline to the final 3D array.

4D Cardiac Segmentation of the Epicardium and Left Ventricle

This work is motivated by the limitations of current techniques to visualize the heart as it moves under contraction and respiration during interventional procedures such as ablation of atrial fibrillation. Our long-term goal is to integrate high resolution models routinely obtained from pre-procedure imaging (here, via MRI) with the low resolution, sparse, images, along with a few scalar measurements such as ECG, which are feasible during the real-time procedure. A key ingredient to facilitate this integration is the extraction from the pre-procedure model of an individualized, low complexity, dynamic model of the moving and beating heart. This is the immediate goal we address here. Our approach stems from work on distributed parameter dynamical systems and uses a combination of truncated basis expansions to obtain the requisite four dimensional low order model. The method's potential is illustrated not only by modeling results but also by estimation of an arbitrary slice from the parameterized model.

/pdf/low-order-4d-dynamical-modeling-of-heart-motion-under-l80v83b9r2.pdf

Gilead Tadmor

Papers

Global Stability Analysis for Linear Dynamics

Analog loop shifting in H 2 optimization of input-delay sampled-data systems

Periodic systems with drift. I. Modeling and identification

4D Cardiac Segmentation of the Epicardium and Left Ventricle

Low-order 4D dynamical modeling of heart motion under respiration