Control of Turbulent and Magnetohydrodynamic Channel Flows

Turbulent flows modeled by systems of partial differential equations are often unstable and can typically be controlled or measured only from the boundary or walls of the flow domain. 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 in turbulence control, aerodynamics, weather forecasting, chemical processes, and plasma control. Topics and Features: * Use of a unique "backstepping" approach to parabolic partial differential equations, which yields not only the stabilization of the flow, but also the explicit solvability of the closed-loop system. * Discussion of hydrodynamics of the turbulent motions modeled by Navier-Stokes partial differential equations. ]* Introduction of control and state estimation designs for flows that include thermal convection and electric conductivity. * Presentation of a new result in fluid dynamics and the analysis of Navier-Stokes equations: closed-form expressions for the solutions of linearized Navier-Stokes equations under feedback. * Extension of the backstepping approach to eliminate one of the well-recognized root causes of transition to turbulence. This monograph is an excellent reference for a broad, interdisciplinary engineering and mathematics audience: control theorists, fluid mechanicists, mechanical engineers, aerospace engineers, chemical engineers, electrical engineers, applied mathematicians, as well as research and graduate students in the above areas. The book may also be used as a supplementary text for graduate courses on control of distributed-parameter systems and on flow control.