A device for controlling an industrial system comprises an input block and a reference value predicter. The reference value predicter includes a disturbance predicter, a state predicter, and a model parameter predicter. A model updater updates the model of the industrial system based on the predicted state and the predicted parameters. A one-prediction-step calculator of the reference value predicter calculates a prediction step based on the predicted disturbances and the model of the system. The device further includes a matrix updater and a linear solver that includes a memory structure such that each row of Jacobian and gradient matrices may be processed in parallel, a pivot search block that determines a maximum element in a column of the Jacobian and gradient matrices, and a pivot row reading block. Moreover, the device further includes a solution updater that updates the solution for an iteration step and controls the iteration process and an output block that sends a solution to the industrial system.