In this talk we address the control of Partial Differential equations (PDEs) with unknown parameters. Our objective is to devise an efficient algorithm capable of both identifying and controlling the unknown system. We assume that the desired PDE is observable provided a control input and an initial condition. Given an estimated parameter configuration, we compute the corresponding control using the State-Dependent Riccati Equation (SDRE) approach. Subsequently, we observe the trajectory and estimate a new parameter configuration using Bayesian Linear Regression method. This process iterates until reaching the final time, incorporating a defined stopping criterion for updating the parameter configuration. The systems arising from the discretization of PDEs are high dimensional, therefore we also focus on the computational cost of the algorithm. The Proper Orthogonal Decomposition (POD), a Model Order Reduction technique, is applied to the system in order to reduce the computational cost of the control computation step, and this provides impressive speedups. We present numerical examples to show the accurateness of the proposed method.