Complexity reduced explicit model predictive control by solving approximated mp-QP program

In this paper, two methods to reduce the complexity of multi-parametric programming model predictive control are proposed. We show that the standard multi-parametric programming problem can be modified by approximating the quadratic programming constraints. For a certain control sequence, only constraints on the first element is considered, while constraints on future elements are ignored or approximated to a simple saturation function. Both the number of critical regions and the computation time are proven to be reduced. Geometric interpretations is given and complexity analysis is conducted. The result is tested on an illustrating example to show its effectiveness.