Constrained MPC Control Based on Reversed Solving Method for Multipliers and its Application

An algorithm of reversed solving method for multipliers is proposed for solving quadratic programming problems of predictive controllers in this paper. Firstly, A Lagrange multiplier, transformed by the objective function and the variable constraints, is treated as the standard form of the quadratic programming (abbr. QP) of decision variables, and then a reversed solving method for multipliers is presented to obtain the approximate solution of the Lagrange multipliers which is used to obtain the solution of the control sequence. Compared with the conventional solving method for QP, the proposed method for multipliers can significantly improve the efficiency of solutions on the guarantee of solving accuracy. Secondly, the proposed algorithm is realized in the design of an vehicle trajectory tracking MPC controller, in which the decision variables of vehicle such as driving safety and comfort, are considered into the system model and they are as output constraints, and the physical limitation of the front-wheel corner is as an input constraint. Finally, the practicality of the proposed algorithm is verified by the vehicle trajectory tracking experiments.