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We consider linear feedback control of the two-dimensional flow past a cylinder at low Reynolds numbers, with a particular focus on the optimal placement of a single sensor and a single actuator. To accommodate the high dimensionality of the flow we compute its leading resolvent forcing and response modes to enable the design of H2-optimal estimators and controllers. We then investigate three control problems: i) optimal estimation (OE) in which we measure the flow at a single location and estimate the entire flow; ii) full-state information control (FIC) in which we measure the entire flow but actuate at only one location; and iii) the overall feedback control problem in which a single sensor is available for measurement and a single actuator is available for control. We characterize the performance of these control arrangements over a range of sensor and actuator placements and discuss implications for effective feedback control when using a single sensor and a single actuator. The optimal sensor and actuator placements found for the OE and FIC problems are also compared to those found for the overall feedback control problem over a range of Reynolds numbers. This comparison reveals the key factors and conflicting trade-offs that limit feedback control performance.
An investigation of optimal feedback controllers performance and robustness is carried out for vortex shedding behind a 2D cylinder at low Reynolds numbers. To facilitate controller design, we present an efficient modelling approach in which we utili
The choice and placement of sensors and actuators is an essential factor determining the performance that can be realized using feedback control. This determination is especially important, but difficult, in the context of controlling transitional fl
The present article represents part of the PhD. dissertation by C. Josserand. We discuss the nucleation of quantized vortices in the nonlinear Schr{o}dinger equation (NLS) for a flow around a disk in two spatial dimensions. It appears that the vortic
Unsteady laminar vortex shedding over a circular cylinder is predicted using a deep learning technique, a generative adversarial network (GAN), with a particular emphasis on elucidating the potential of learning the solution of the Navier-Stokes equa
Wireless sensor-actuator networks offer flexibility for control design. One novel element which may arise in networks with multiple nodes is that the role of some nodes does not need to be fixed. In particular, there is no need to pre-allocate which