  The nonlinear robustness of laminar plane Couette flow is considered under
the action of in-phase spanwise wall oscillations by computing properties of
the edge of chaos, i.e., the boundary of its basin of attraction. Three
measures are used to quantify the chosen control strategy on
laminar-to-turbulent transition: the kinetic energy of edge states (local
attractors on the edge of chaos), the form of the minimal seed (least energetic
perturbation on the edge of chaos), and the laminarization probability (the
probability that a random perturbation from the laminar flow of given kinetic
energy will laminarize). A novel Bayesian approach is introduced to enable the
accurate computation of the laminarization probability at a fraction of the
cost of previous methods. While the edge state and the minimal seed provide
useful information about the dynamics of transition to turbulence, neither
measure is particularly useful to judge the effectiveness of the control
strategy since they are not representative of the global geometry of the edge.
In contrast, the laminarization probability provides global information about
the edge and can be used to evaluate the control effectiveness by computing a
laminarization score (the expected laminarization probability) and the
associated expected dissipation rate of the controlled flow. These two
quantities allow for the determination of optimal control parameter values
subject to desired constraints. The results discussed in the paper are expected
to be applied to a wide range of transitional flows and control strategies
aimed at suppressing or triggering transition to turbulence.
