In this study, fed-batch cultures of a Pichia pastoris strain constitutively expressing a single chain antibody fragment (scFv) under the control of the glyceraldehyde-3-phosphate dehydrogenase (GAP) promoter were performed in a pilot 50 L bioreactor. Due to the very high cell density achieved within the first 75 h, typically between 140 and 160 g-DCW/L of dry cell weight (DCW), most of the scFv is produced under hard oxygen transfer limitation. To improve scFv productivity, a direct adaptive dissolved oxygen (DO)-stat feeding controller that maximizes glycerol feeding under the constraint of available oxygen transfer capacity was developed and applied to this process. The developed adaptive controller enabled to maximize glycerol feeding through the regulation of DO concentration between 3 and 5 % of saturation, thereby improving process productivity. Set-point convergence dynamics are characterized by a fast response upon large perturbations to DO, followed by a slower but very robust convergence in the vicinity of the boundary with almost imperceptible overshoot. Such control performance enabled operating closer to the 0 % boundary for longer periods of time when compared to a traditional proportional-integral-derivative algorithm, which tends to destabilize with increasing cell density.