We describe a fast continuous optimization wavefront shaping system able to focus light through dynamic scattering media. A micro-electro-mechanical system-based spatial light modulator, a fast photodetector, and field programmable gate array electronics are combined to implement a continuous optimization of a wavefront with a single-mode optimization rate of 4.1 kHz. The system performances are demonstrated by focusing light through colloidal solutions of TiO2 particles in glycerol with tunable temporal stability.