Recent experimental studies have demonstrated the possibility of information storage in short antiferromagnetic chains on an insulator substrate [S. Loth et al., Science 335, 196 (2012)]. Here, using the density functional theory and atomistic spin dynamics simulations, we show that a local magnetic control of such chains with a magnetic tip and magnetic pulses can be used for fast switching of their magnetization. Furthermore, by changing the position of the tip one can engineer the magnetization dynamics of the chains.