Flow control plays a vital role in improving efficiency in aerospace, maritime, and energy systems by delaying transition to turbulence and suppressing instabilities such as Tollmien–Schlichting waves. This work uses the Kuramoto–Sivashinsky (KS) equation as a model to study convective instabilities in boundary layers. A finite-difference discretization yields a state-space formulation, enabling systematic application of control strategies. Linear Quadratic Regulator (LQR) and adjoint-based optimization methods are developed to minimize flow perturbations. Results show LQR effectively suppresses disturbances, while adjoint-based control scales efficiently to nonlinear cases, highlighting promising avenues for future turbulence management.