Interior Point Solution of Multilevel Quadratic Programming Problems in Constrained Model Predictive Control Applications

This paper examines the use of an interior point strategy to solve multilevel optimization problems that arise from the inclusion of the closed-loop response of constrained, linear model predictive control (MPC) within a primary quadratic or linear programming problem. We motivate the formulation through its application to optimizing control problems, although the strategy is applicable to several problem types. The problem is cast as a dynamic optimization problem in which an optimal steady-state operating point is sought, subject to constraints on the closed-loop response of the system under constrained predictive control. Because a quadratic programming (QP) problem must be solved at every sampling period, the resulting problem is multilevel in nature. The formulation approach used in this paper is to include the Karush−Kuhn−Tucker (KKT) conditions that correspond to the MPC quadratic programming subproblems as constraints within a single-level optimization problem. The resulting complementarity constrained optimization problem is shown to be reliably and efficiently solved using an interior point approach. The method is applied to two case studies, and its performance is compared to an alternative mixed-integer programming solution approach.