In this disclosure, equations to be solved in the model predictive control are transformed by using an off-line algebraic simplification method into a matrix operational expression representing a product of a coefficient matrix and a vector regarding solution inputs within a control horizon is equal to a function vector regarding target values of output states and the output states. The size of the coefficient matrix is reduced compared with the conventional matrix. Then, the matrix operational expression is solved in an online plant control apparatus with present output states and present target values of the output stats of a plant to be controlled, by the direct method, to output the solution to the plant.