Multiple use of the fractional-order differential calculus in the model predictive control

In the paper a multiple use of the fractional-order differential calculus theory in the model predictive control is proposed. First, the principle of the integer-order linear predictive control and theoretical foundations of the fractional-order differential calculus are reminded. Using the presented theoretical foundations attention is focused further on the possibility of developing the fractional-order model predictive control with an internal process model and a fractional-order cost function. The introduction of the fractional-order differential calculus at the stage of synthesizing the control algorithm offers an additional degree of freedom in tuning a control loop. The discussion is illustrated with results of some laboratory experiments.