In the classical approach to control, a mathematical model of the plant (in state-space, transfer function, etc. form) and a performance criterion are used in order to come up with a mathematical description of a controller to be used in achieving the control objectives. In the data-driven approach, instead, one trajectory of the plant variables is given, together with the performance criterion; the objective is to compute from this data a suitable control input signal.

In this talk we concentrate on the discrete-time finite-horizon quadratic control problem with prescribed "initial conditions", given in the form of a prefix of a trajectory which needs to be extended over the whole time-interval so as to minimize the cost. We give a solution of this problem, and we illustrate some results of our data-driven investigation. Among these is an intrinsic justification of the optimality of the state-feedback control input law which is prominent in the state-space approach; we show that this fact can be established from first principles, and is not only a consequence of the use of state-space representations.