The norm \(\left\Vert \underline{\mathcal {S}}(H,K)\right\Vert \) can be used to represent the weighted sum associated with the cost functional that needs to be optimized by the designed control policy. A natural extension to other optimal control problems arises depending on different choices of this norm. This chapter focuses on two particular extensions– \(\mathcal {H}_2\) and \(\mathcal {H}_{\infty}\) optimal control–as well as an introduction to stochastic optimal control via the linear quadratic Gaussian (LQG) framework.