B Protas 2008 Nonlinearity 21 R203 doi:10.1088/0951-7715/21/9/R01
B Protas
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In this article we review the state of the art in the field of control of vortex dynamics. We focus on problems governed by two-dimensional incompressible Euler equations in domains both with and without boundaries. Following a comprehensive review of earlier approaches, we discuss how methods of modern control and optimization theory can be employed to solve control problems for vortex systems. In addition, we address the companion problem of the state estimation for vortex systems. While most of the discussion concerns point vortex systems, in the second part of the article we also introduce a novel approach to the control of Euler flows involving finite-area vorticity distributions. The article concludes with what, in the author's opinion, represent promising new research directions.
76D55 Flow control and optimization (See also 49Q10, 93C20, 93C95)
Issue 9 (September 2008)
Received 16 February 2008, in final form 28 May 2008
Published 21 July 2008
B Protas 2008 Nonlinearity 21 R203
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