Our ability to design efficient technologies involving complex fluid flows strongly depends on our ability to actively control these flows in real-time in an autonomous fashion, according to our needs. To date most flow control strategies arepassive and are inefficient, both from operational costs and achievable performance point of view. In this talk we will describe the computational challenges oneface in feedback control of multi-scale fluid flows, wide range of spatial and temporal scales that are tightly coupled, using a spatially distributed network ofsensors, actuators and controllers. Two prototype systems (1) partial differential equations with trigonometric nonlinearity, exhibiting soliton behavior and (2)rotating Rayleigh-Benard convection with an embedded chaotic attractor will be considered in the talk. Various optimal controllers that work effectively in the presence of uncertainty are designed and tested in the direct numerical simulations.
Collocation spectral methods based on Fourier modes are used for the numerical computations. Nonlinear matrix Riccati equation is central to various control designs, solution of this is got using Eigenvalue and Schur decomposition, with and without balancing. H_2 norm is computed numerically using its time domain characterization in terms of gramians and avoiding costly improper integrals. H_infinitynorm is computed using an iteration procedure involving Hamiltonian matrix. The numerical results indicate various surprising things and nicely illustrate the intricacies involved in dealing with full Navier-Stokes equations.