How to tackle a linear quadratic control problem with unknown time-varying parameters in objective funtion, e.g., a problem with a simple state dynamic $x_{t+1}=x_{t}+u_{t}$ and cost function $$ \sum_{t=1}^{T}x_{t}^{\top}Q_{t}x_{t}+u_{t}^{\top}R_{t}u_{t}+x_{t}^{\top}N_{t}u_{t} $$ where $Q_{t}$, $R_{t}$ and $N_{t}$ could be time-varying or non-stationary but unknwon and they need to be estimated.
Are there any research papers or books talking about this topic?
I myself found a paper that maybe useful for future readers: Online Linear Quadratic Control enter link description here.
See also the references therein and citing papers.