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

Preview control and fixed-lag smoothing allow an anti-causal component in the controller/estimator. Time domain variational analysis is used in a reduction to an open loop differential game, leading to a complete, necessary and sufficient characterization of suboptimal values and an explicit state space design, in terms of a parameterized (non-standard) algebraic matrix Riccati equation in a general continuous time linear system setting. The solution offers insight into the appropriate structure of the associated Hamiltonian, where the state and co-state are not the usual state of the original dynamic system and that of its adjoint. Rather, the state and co-state are selected to capture the respective lumped effects of initial data and future input selection in the allied game.

/pdf/h-sub-spl-infin-preview-control-and-fixed-lag-smoothing-i-3pnufx95wo.pdf

H/sub /spl infin// preview control and fixed-lag smoothing I: matrix ARE solutions in continuous-time systems

The following phenomenon is specific to a class of hereditary control systems: Trajectories of these systems can be stabilized (i.e., controlled to asymptotically approach the origin). However, it is impossible to obtain stabilization with controls whose rate of decay is the same as that of the trajectories. We call such systems trajectory stabilizable. We characterize the class of trajectory stabilizable systems and present both open and closed loop trajectory-stabilizing schemes. The controllability aspect of trajectory stabilizability is studied too. Examples illustrate the discussion.

Trajectory stabilizing controls in hereditary linear systems

Low order Galerkin models were originally introduced as an effective tool for stability analysis of fixed points and, later, of attractors, in nonlinear distributed systems. An evolving interest in their use as low complexity dynamical models, goes well beyond that original intent. It exposes often severe weaknesses of low order Galerkin models as dynamic predictors and has motivated efforts, spanning nearly three decades, to alleviate these shortcomings. Transients across natural and enforced variations in the operating point, unsteady inflow, boundary actuation and both aeroelastic and actuated boundary motion, are hallmarks of current and envisioned needs in feedback flow control applications, bringing these shortcomings to even higher prominence. Building on the discussion in our previous chapters, we shall now review changes in the Galerkin paradigm that aim to create a mathematically and physically consistent modeling framework, that remove what are otherwise intractable roadblocks. We shall then highlight some guiding design principles that are especially important in the context of these models. We shall continue to use the simple example of wake flow instabilities to illustrate the various issues, ideas and methods that will be discussed in this chapter.

/pdf/galerkin-models-enhancements-for-flow-control-1n8smjk2jx.pdf

Galerkin Models Enhancements for Flow Control

Active flow control is used to modify the lift, drag and pitching moments on a semicircular wing with aspect ratio, AR = 2, and chord Reynolds number is 68,000. The wing is mounted on a pitch/plunge sting mechanism that responds to the instantaneous loads and moments acting on the wing. The leading edge of the airfoil contains 16 spatially localized actuators that can be independently controlled. Smoke wire visualization, surface pressure and six-component force balance measurements are used to characterize the effects of openloop forcing. The lift coefficients on the steady wing are enhanced with the actuation, similar to the effect of dynamic stall vortex lift enhancement that occurs during a pitch up maneuver. Surface pressure measurements are being used to construct a flow model for use in feedback control. Progress toward the goal of designing a feedback controller to stabilize the flight of the model in an oscillatory freestream is discussed.

/pdf/control-of-flow-structure-on-a-semi-circular-planform-wing-2brtffhnik.pdf

Control of Flow Structure on a Semi-Circular Planform Wing

The paper examines the effects of (low) switching frequency and delays on a closed loop system with pulse-width modulated (PWM) components. A modeling procedure is described together with analytical formulas. Deviations from standard (idealized) models which replace a PWM unit with a fixed gain are quantified. Low switching frequency reduces the effective PWM gain, and delays make the gain larger than the idealized one at low voltages. The necessary and sufficient condition for existence of a T-periodic stable equilibrium in the closed loop linear system with a PWM is obtained. This result is based on an analysis of a piecewise affine discrete-time map under the assumption of linear-ripple approximation. Experimental results are provided for a PWM controlled dc servo motor, while analytical results are presented for certain examples from the power electronics literature.

Gilead Tadmor

Papers

H/sub /spl infin// preview control and fixed-lag smoothing I: matrix ARE solutions in continuous-time systems

Trajectory stabilizing controls in hereditary linear systems

Galerkin Models Enhancements for Flow Control

Control of Flow Structure on a Semi-Circular Planform Wing

Effects of finite switching frequency and delay on PWM controlled systems