title: On the control of the chaotic attractors of the 2-d Navier-Stokes equations.
abstract: The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equations (ODEs). The dynamics of the fifth-order system was studied by analyzing the system's attractor for different values of Reynolds number, Re. Then, control laws are proposed to drive the states of the ODE system to a desired attractor. Finally, an adaptive controller is designed to synchronize two reduced order ODE models having different Reynolds numbers and starting from different initial conditions. Simulation results indicate that the proposed control schemes work well.
authors.affiliation: Department of Mathematics, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait.
authors.forename: Nejib
authors.initials: N
authors.lastname: Smaoui
authors.affiliation: Department of Electrical Engineering, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait.
authors.forename: Mohamed
authors.initials: M
authors.lastname: Zribi