Optimal and robust control and estimation of transition, convection, and turbulence

The large increases in drag, cyclic structural loading, internal stresses, mixing, and heat transfer caused by turbulence in flows of engineering interest have motivated engineers to study turbulence and attempt to alter its effects. Recent advances in MEMS capabilities may soon make it possible to measure small-scale turbulent fluctuations of a flow and, subsequently, to apply coordinated small-scale forcing to the flow in order to achieve a desired large-scale effect. The present work attempts to develop techniques to derive the necessary control strategies for such control problems from first principles, leveraging our knowledge of the Navier-Stokes equation which governs these flows and our ability to simulate this equation accurately in simple configurations. By so doing, we bypass the ad hoc assumptions about the turbulence dynamics often used to determine such control strategies and develop several new tools for analysis of flow systems in the control setting.; Approaching this difficult problem in steps of gradually increasing complexity, optimal and robust control theories are used in the present work to derive and demonstrate effective control and estimation strategies for three important model problems in fluid mechanics. The model problems considered are: (1) the application of linear optimal/robust control theory to the linear paths to transition in a plane channel, (2) the application of linear optimal/robust control theory to a low-order nonlinear chaotic convection problem, and (3) the application of optimal control theory in a DNS-based predictive control setting to the fully nonlinear problem of turbulence.; In order to develop feedback algorithms for practical (disturbed) environments, it is recognized that a degree of robustness will be necessary in the control rules. In the final section of this work, a general framework for robust control for problems governed by the Navier-Stokes equation is established by mathematical analysis, laying the foundation for much of our future work in this area.