High fidelity, low dimensional model and control development for complex flow fields is a challenging yet highly rewarding research topic. The systematic modeling and control approach developed in this paper is applied to suppress optical distortions caused by large scale density variations in a free, unstable shear layer behind a backward facing step. Simulations of an unforced and open-loop forced shear layer, based on the compressible Navier-Stokes equations, are used to compile a flow state database to formulate a linear basis set using proper orthogonal decomposition. It is shown that nonlinear auto regressive exogenous models accurately predict the fundamental behavior and forcing interaction of the POD time coefficients. This low dimensional model allows for simulation of open and closed loop dynamics, prediction of future flow states, and is ultimately utilized to develop feedback control algorithms. Feedback results using nonlinear, adaptive regulation of the vortex shedding phenomenon indicate that a 35 per cent reduction in the optical aberrations is achieved.