An optimization algorithm dedicated to a MPC problem for discrete time bilinear models

Abstract

This paper describes an algorithm for solving the optimization problem which occurs in a model-based predictive control (MPC) algorithm for discrete time bilinear models. This optimization problem is nonlinear in general, because the model acts as a nonlinear equality constraint. Common approaches of performing such a nonlinear optimization problem boil down to (successively) approximating the nonlinear objective function, followed by performing a line search. In this paper it is demonstrated that the structural properties of the bilinear state space model enable to formulate the nonlinear optimization problem as a sequence of quadratic programming problems which exactly represent the original objective function, implying that no additional line search is needed. The proposed optimization algorithm is compared to one that is based on linearization around an input trajectory. To benefit from the advantages of both algorithms, a hybrid algorithm is proposed, which outperforms the other two in most cases.