Control of Turbulent and Magnetohydrodynamic Channel Flows: Boundary Stabilization and State Estimation [Hardcover]

Thermal-Fluid Convection Loop: Boundary Stabilization.- Thermal-Fluid Convection Loop: Boundary Estimation and Output-Feedback Stabilization.- 2D NavierStokes Channel Flow: Boundary Stabilization.- 2D NavierStokes Channel Flow: Boundary Estimation.- 3D Magnetohydrodynamic Channel Flow: Boundary Stabilization.- 3D Magnetohydrodynamic Channel Flow: Boundary Estimation.- 2D NavierStokes Channel Flow: Stable Flow Transfer.- Open Problems.

This monograph presents new constructive design methods for boundary stabilization and boundary estimation for several classes of benchmark problems in flow control, with potential applications to turbulence control, weather forecasting, and plasma control. The basis of the approach used in the work is the recently developed continuous backstepping method for parabolic partial differential equations, expanding the applicability of boundary controllers for flow systems from low Reynolds numbers to high Reynolds number conditions.

Efforts in flow control over the last few years have led to a wide range of developments in many different directions, but most implementable developments thus far have been obtained using discretized versions of the plant models and finite-dimensional control techniques. In contrast, the design methods examined in this book are based on the continuum version of the backstepping approach, applied to the PDE model of the flow. The postponement of spatial discretization until the implementation stage offers a range of numerical and analytical advantages.

Specific topics and features:

* Introduction of control and state estimation designs for flows that include thermal convection and electric conductivity, namely, flows where instability may be driven by thermal gradients and external magnetic fields.

* Application of a special backstepping approach where the boundary control design is combined with a particular Volterra transfolÓ"