Feedback Control of Turbulent Shear Flows by Genetic Programming

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  title =        "Feedback Control of Turbulent Shear Flows by Genetic
  author =       "Thomas Duriez and Vladimir Parezanovic and 
                 Kai von Krbek and Jean-Paul Bonnet and Laurent Cordier and 
                 Bernd R. Noack and Marc Segond and Markus Abel and 
                 Nicolas Gautier and Jean-Luc Aider and 
                 Cedric Raibaudo and Christophe Cuvier and Michel Stanislas and 
                 Antoine Debien and Nicolas Mazellier and Azeddine Kourta and 
                 Steven L. Brunton",
  year =         "2015",
  month =        may # "~05",
  note =         "Comment: 49 pages, many figures, submitted to Phys Rev
  abstract =     "Turbulent shear flows have triggered fundamental
                 research in nonlinear dynamics, like transition
                 scenarios, pattern formation and dynamical modelling.
                 In particular, the control of nonlinear dynamics is
                 subject of research since decades. In this publication,
                 actuated turbulent shear flows serve as test-bed for a
                 nonlinear feedback control strategy which can optimise
                 an arbitrary cost function in an automatic
                 self-learning manner. This is facilitated by genetic
                 programming providing an analytically treatable control
                 law. Unlike control based on PID laws or neural
                 networks, no structure of the control law needs to be
                 specified in advance. The strategy is first applied to
                 low-dimensional dynamical systems featuring aspects of
                 turbulence and for which linear control methods fail.
                 This includes stabilising an unstable fixed point of a
                 nonlinearly coupled oscillator model and maximising
                 mixing, i.e.\ the Lyapunov exponent, for forced Lorenz
                 equations. For the first time, we demonstrate the
                 applicability of genetic programming control to four
                 shear flow experiments with strong nonlinearities and
                 intrinsically noisy measurements. These experiments
                 comprise mixing enhancement in a turbulent shear layer,
                 the reduction of the recirculation zone behind a
                 backward facing step, and the optimised reattachment of
                 separating boundary layers. Genetic programming control
                 has outperformed tested optimised state-of-the-art
                 control and has even found novel actuation
  bibsource =    "OAI-PMH server at",
  oai =          "",
  keywords =     "genetic algorithms, genetic programming, physics -
                 fluid dynamics",
  URL =          "",

Genetic Programming entries for Thomas Duriez Vladimir Parezanovic Kai A F F von Krbek Jean-Paul Bonnet Laurent Cordier Bernd R Noack Marc Segond Markus W Abel Nicolas Gautier Jean-Luc Aider Cedric Raibaudo Christophe Cuvier Michel Stanislas Antoine Debien Nicolas Mazellier Azeddine Kourta Steven L Brunton