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

Open- and closed-loop control of vortex shedding in two-dimensional flow over a flat plate at high angles of attack is numerically investigated at a Reynolds number of 300. Unsteady actuation is modeled as a body force near the leading or trailing edge, and is directed either upstream or downstream. For moderate angles of attack, sinusoidal forcing at the natural shedding frequency results in phase locking, with a periodic variation of lift at the same frequency. However, at sufficiently high angles of attack, subharmonics of the forcing frequency are also excited and the average lift over the forcing period varies from cycle to cycle in a complex manner. It is observed that the periods with the highest averaged lift are associated with particular phase difference between the forcing and the lift. We design a feedback algorithm to lock the forcing with the phase shift associated with the highest period-averaged lift. It is shown that the compensator results in a stable phaselocked limit cycle for a larger range of forcing frequencies than the open-loop control, and that it is able to stabilize otherwise unstable high-lift limit cycles that cannot be obtained with open-loop control. For example at an angle of attack of 40 ◦ , the feedback controller can increase the averaged lift coefficient from 1.35 to 2.43, an increase of 80%.

/pdf/closed-loop-control-of-vortex-shedding-on-a-two-dimensional-3avqpwb59v.pdf

Closed-Loop Control of Vortex Shedding on a Two-Dimensional Flat-Plate Airfoil at a Low Reynolds Number ∗

$H_\infty $ optimal control and system design problems are known to mathematically reduce to the framework of operator interpolation. Here a solution scheme in the context of systems with multiple input lags is provided. The main result, a linear algebraic characterization of eigenvalue/eigenfunction pairs, can be utilized also in finite-dimensional approximations of the associated Hankel Operator. A particular feature of the analysis is the heavy reliance on time-domain techniques and utilization of explicit time-domain properties of the transfer function.

H ∞ interpolation in systems with commensurate input lags

The mitigation of oscillatory vortex shedding behind a cylinder is chosen as a well-investigated benchmark problem to compare model-based feedback flow control approaches. The flow is sensed by a single velocity signal in the wake and is manipulated via a single volume force actuator. A low-dimensional proper orthogonal decomposition Galerkin model is adopted as a control-oriented fluid flow representation. An extended Kalman filter is used as an effective means for online dynamic state estimation. Investigated strategies of linear and nonlinear controller design include pole placement, linear parameter-varying, input–output linearization, Lyapunov-based backstepping, and nonlinear model predictive control. These strategies are applicable to a large class of flows with oscillatory dynamics and to experimental conditions, where variants have already been used. Controllers are evaluated and compared based on their application to the full plant, that is, to the direct numerical simulation of the wake, emulating an experiment with a single hot-wire sensor. Overall, nonlinear closed-loop control is shown to be distinctly superior to linear approaches. As is often the case, physics dictates a similarity of successful control commands, irrespective of the design approach, and differentiates these controllers, as a group, from less successful approaches.

On the need of nonlinear control for efficient model-based wake stabilization

A major roadblock in taking full advantage of the recent exponential growth in data collection and actuation capabilities stems from the curse of dimensionality Simply put, existing techniques are ill-equipped to deal with the resulting overwhelming volume of data The goal of this chapter is to show how the use of simple dynamical systems concepts can lead to tractable, computationally efficient algorithms for extracting information sparsely encoded in multimodal, extremely large data sets In addition, as shown here, this approach leads to nonentropic information measures, better suited than the classical, entropy-based information theoretic measure, to problems where the information is by nature dynamic and changes as it propagates through a network where the nodes themselves are dynamical systems

/pdf/the-role-of-dynamics-in-extracting-information-sparsely-1ki3a01762.pdf

The Role of Dynamics in Extracting Information Sparsely Encoded in High Dimensional Data Streams

The problem of sampled-data H2 control of systems with a single input delay is studied. Conventional solutions of sampled-data optimal control problems begin with a conversion to a discrete-time problem with input delays, followed by a matching optimization method, geared to handle delays. We propose reversing 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.

Gilead Tadmor

Papers

Closed-Loop Control of Vortex Shedding on a Two-Dimensional Flat-Plate Airfoil at a Low Reynolds Number ∗

H ∞ interpolation in systems with commensurate input lags

On the need of nonlinear control for efficient model-based wake stabilization

The Role of Dynamics in Extracting Information Sparsely Encoded in High Dimensional Data Streams

Sampled-Data $H^{2}$ Optimization of Systems With I/O Delays via Analog Loop Shifting