LQ optimal controllers are widely used in many applications as they provide a simple and effective solution to optimal control problems. There are many examples in the literature that show the lack of robustness of such controllers when the process is subject to parameter variations or when some dynamics are neglected. The hybrid algorithms proposed in this work extend the family of model reference minimal control synthesis adaptive controllers and address the issue of enhancing the robustness of LQ regulators. The main idea behind the approach is to seek a simple and alternative route to implement the LQ regulator via the MCS algorithm which is effective also in those practical cases when the LQ action itself fails. The stability of all the proposed control schemes is proved and the performance on a set of representative examples shows the effectiveness of the approach.