Model Predictive Control Using Input Signal Approximated by Cubic LSE Splines

In this paper, classical model predictive algorithm was revisited and it was reformulated in terms of lse-splines to accelerate the algorithm. To this end, model predictive control law and the underlying constrained optimization problem were recast in terms of the coefficients of a compact set of lse-splines. Since lse-splines are not required to pass all discrete-time values of control signal, it was shown that the compact set of lse-splines is minimal. Thereby, time-complexity of model predictive control and size of the underlying constrained optimization problem were minimized. It was shown that solution of the constrained optimization problem can be accelerated and real-time application of model predictive control is possible. Four-tank bench-marking problem was used to investigate performance of the model predictive control.