Techniques for optimizing automated drilling processes are disclosed. Such techniques include modeling a formation and selecting a drilling trajectory in the formation. Measurements of rate of penetration (ROP), revolutions per minute (RPM), weight-on-bit (WOB) and torque-on-bit (TOB) of a drilling string at a position on the drilling trajectory in the formation are received. A functional relationship between depth of cut (DOC), WOB, and TOB for the modeled formation is determined. Operating constraints defining a safe operating envelope as a function of RPM and WOB along the selected drilling trajectory are determined, and an optimal RPM and WOB is determined based on operating constraints. A cost function of RPM and WOB is determined, and a path from current RPM and WOB to optimal RPM and WOB is determined based on the cost function.