Performance of adaptive optics systems relies on the type of controller used for perturbation correction, especially when perturbations exhibit complex temporal spectra, e.g., energetic low temporal frequencies due to windshake, or vibrations affecting the system.

High performance control accounts for complex spectra to design efficient AO controllers. These are based on hypothesis on the perturbation to be compensated and on the measurement noise. In this presentation, I will explain how is build a linear quadratic Gaussian (LQG) controller, how its performance criterion is related to image quality, how perturbation and noise models enter the design. I will also present on-sky SCAO and wide field results with a comparison between standard controllers and LQG, and show the influence of some model parameters on the on-sky performance.