The Gran Telescopio Canarias (GTC) is being equipped with an Adaptive Optics (AO) system, developed by the Instituto de Astrofísica de Canarias (IAC). The Institut d'Optique Graduate School-Laboratoire Charles Fabry (IOGS-LCF), through a collaboration with the IAC, integrated some high performance control solutions. In this proceeding, we present the first and promising on-sky results on a 10-meter class telescope for such a controller, namely a full Linear Quadratic Gaussian regulator (LQG). We start with a brief description of the GTCAO system, including the data-driven LQG regulator construction. Performance results are then presented with a full LQG regulator in line with the previous on-bench experiments, implemented in DARC, the GTCAO RTC. A comparison is performed with the integrator, the baseline controller, through the comparison of point spread functions acquired on the scientific camera and residual slopes recorded by the wavefront sensor.