Model Predictive Control Using First/Third Order Splines

Model predictive control is performed by solving a constrained optimization problem at every time step. Since, this optimization problem is a function of the control signal in the prediction horizon, long prediction horizon for large-scale plant model is not practical for model predictive control applications. However, it can be shown that when the control signal sampled by a coarse time step is represented with linear or cubic splines, these splines can be used to interpolate control signal series to calculate the missing data values. Hence, it can be shown that control signal is a function of the coefficients of splines. Using this fact, it is shown that the quadratic optimization defined in terms of control signal can be replaced by a new optimization problem defined in terms of the coefficients of splines. Thereby, it is shown that the size optimization problem can be reduced and model predictive control can be accelerated in order of magnitudes.