It is possible under limited conditions. The Linear-quadratic regulator (LQR) controller assumes that the system under control has linear dynamics and that the transition and observation models are deterministic. While in practice it works if these conditions are violated, the more extreme the violation the more likely it is to fail.
An alternative is the Linear-quadratic-gaussian controller because it allows for noise in the motions and percepts. A challenge with using LQG is that you must have model of the noise.
More specifically, assume you have the following dynamical model:
$\dot{\mathbf{x}}(t) = A\mathbf{x}(t) + B\mathbf{u}(t) + \mathbf{v}(t), \mathbf{v}(t) \sim \mathcal{N}(0, M) \\
\mathbf{y}(t) = C\mathbf{x}(t) + \mathbf{w}(t), \mathbf{w}(t) \sim \mathcal{N}(0, N)$
where $\mathbf{x}(t)$, and $\mathbf{u}(t)$ represent the state of the system and the control applied to at it at time $t$ respectively, $A$, $B$, and $C$ represent the natural dynamics, the control dynamics, and the observation dynamics respectively, and finally $\mathbf{v}(t)$ and $\mathbf{w}(t)$ represent noise of the motion and observation models respectively and are zero mean gaussian distributions with covariances $M$ and $N$.
In order to use LQG you need to know $A$, $B$, $C$, $M$, and $N$ as well as the initial state of the system, i.e. $\mathbf{x}(0)$.