The problem of avoiding saturation of the coil currents is critical in large tokamaks with superconducting coils like ITER. Indeed, if the current limits are reached, a loss of control of the plasma may lead to a major disruption. Therefore, a current limit avoidance (CLA) system is essential to operate safely. This paper provides the first experimental evidence that the online solution of a constrained quadratic optimization problem can offer a valid methodology to implement a CLA. Experiments are carried out on the tokamak à configuration variable at the Swiss Plasma Center, showing the effectiveness of the proposed approach and its suitability for real-time application in view of future reactors such as ITER.