Using Ramp Functions to solve LP-based MPC

A new solution strategy, utilizing ramp functions, is proposed for solving LP problems arising in Model Predictive Control. The solution strategy can take a general LP formulation, and avoids the increase in optimization variables resulting from converting the LP problem into standard form. Unlike the simplex method, there is no need to find an initial feasible solution. Numerical experiments demonstrate a significant increase in solution speed compared to the previously proposed ramp-based Simplex [1], and compares favorably to a state-of-the-art commercial solver like CPLEX [2] for small to moderately sized problems.