Optimal and Robust Control and Estimation of Linear Paths to Transition

this paper is not valid. Iterative optimal control approaches over finite time intervals, which make use of full state information, may still be formulated (Abergel & Temam 1990) and performed (Moin & Bewley 1995) with impressive results. In order to make such schemes practical, one must understand how to account for disturbances in a rigorous fashion and how to estimate accurately the necessary components of the state (for instance, the location and strength of the near-wall coherent structures) based on limited flow measurements. The present paper makes these concepts clear in a fluid-mechanical sense, albeit for a linear problem, and thus provides a step in this development. Techniques to extend the robust control concept, introduced for problems in fluid mechanics in the present work, to nonlinear problems (such as turbulence) are discussed in Bewley, Moin, & Temam (1997) and Bewley, Temam, & Ziane (1998). 1.1. Outline of pape