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

A principal challenge in the use of empirical proper orthogonal decomposition (POD) Galerkin models for feedback control design in fluid flow systems is their typical fragility and poor dynamic envelope. Closed loop performance and optimized sensor(s) location are significantly improved by use of interpolated POD modes from a succession of low dimensional models from sections of a controlled transient manifold. This strategy is demonstrated in the benchmark of stabilization of the wake flow behind a circular cylinder.

/pdf/wake-stabilization-using-pod-galerkin-models-with-1bpu9g196y.pdf

Wake stabilization using POD Galerkin models with interpolated modes

Systems with input or output delays form the simplest, and yet one of the most widely applied classes of distributed parameter models. This is a review of some problem-oriented H∞ methods for that class, with an emphasis on computational simplicity. Reviewed methods include operator interpolation, game-theoretic state-space treatments in the time domain, a J-spectral factorization approach, and methods exploiting various ideas from sampled-data theory. Some interesting properties of the (sub)optimal solutions are discussed as well.

http://leo.technion.ac.il/publications/HinfDelayReview/HinfDelayReview.pdf

H∞ control of system with I/O delay: a review of some problem‐oriented methods

We introduce two wavefront-based methods for the inverse problem of electrocardiography, which we term wavefront-based curve reconstruction (WBCR) and wavefront-based potential reconstruction (WBPR). In the WBCR approach, the epicardial activation wavefront is modeled as a curve evolving on the heart surface, with the evolution governed by factors derived phenomenologically from prior measured data. The body surface potential/wavefront relationship is modeled via an intermediate mapping of wavefront to epicardial potentials, again derived phenomenologically. In the WBPR approach, we iteratively construct an estimate of epicardial potentials from an estimated wavefront curve according to a simplified model and use it as an initial solution in a Tikhonov regularization scheme. Initial simulation results using measured canine epicardial data show considerable improvement in reconstructing activation wavefronts and epicardial potentials with respect to standard Tikhonov solutions. In particular the WBCR method accurately finds the anisotropic propagation early after epicardial pacing, and the WBPR method finds the wavefront (regions of sharp gradient of the potential) both accurately and with minimal smoothing

Wavefront-based models for inverse electrocardiography

We propose a system reduction strategy for spectral and Galerkin models of incompressible fluid flows. This approach leads to dynamic models of lower order, based on a partition in slow, dominant and fast modes. In the reduced models, slow dynamics are incorporated as non-linear manifold consistent with mean-field theory. Fast dynamics are stochastically treated and can be lumped in eddy-viscosity approaches. The employed interaction models between slow, dominant and fast dynamics respect momentum and energy balance equations in a mathematically rigorous manner—unlike unsteady Reynolds-averaged Navier–Stokes models or Smagorinsky-type reductions of the Navier–Stokes equation. The proposed system reduction strategy is employed to the cylinder wake benchmark. Copyright © 2009 John Wiley & Sons, Ltd.

http://www.math.le.ac.uk/people/ag153/homepage/NoackSchlegelMorzynskiTadmor.pdf

System reduction strategy for Galerkin models of fluid flows

In the present study the flow around a 2D bluff body with blunt stern is investigated experimentally and theoretically. The goal is to decrease and stabilize drag by active control. Low-dimensional vortex models are used to describe actuation effects on the coherent structures and the pressure field. Open-loop actuation as well as feedback control is applied using robust H ∞-controllers and slope-seeking feedback for a range of Reynolds numbers based on the height from 20 000 to 60 000. As expected, a decreased drag is observed to be related to delayed vortex shedding, i.e. an extended recirculation zone. Intriguingly, a control which mitigates the natural coupling between separating upper and lower shear-layer and the vortex street serves that purpose.

Gilead Tadmor

Papers

Wake stabilization using POD Galerkin models with interpolated modes

H∞ control of system with I/O delay: a review of some problem‐oriented methods

Wavefront-based models for inverse electrocardiography

System reduction strategy for Galerkin models of fluid flows

Feedback Control Applied to the Bluff Body Wake