The polynomial approximation of the explicit solution of model-based predictive controller for drive applications

The complexity of implementing the Explicit solution of Model-based Predictive Control (Exp-MPC) in drive applications results in a higher number of generated regions. This increases the required memory space to store these regions and the coefficients of the associated optimal control laws, even when the solution is implemented using an efficient algorithm like Binary Search Tree (BST). The proposed method aims to replace the optimal linear/affine control laws, defined over several regions of the feasible state space, with one polynomial. The polynomial will be multivariate, with higher order, and defined over a combination of feasible regions. Using the polynomial approximation, the necessary memory space, to store region coordinates and the coefficients of optimal control laws, is reduced significantly. Although the accuracy of the optimal controller is reduced with use of polynomial approximation, it makes the implementation more realistic; provided the stability and the feasibility of the problem is still guaranteed.