When does QP yield the exact solution to constrained NMPC?

Authors

José Mare, University of NewcastleFollow
Jose A. de Dona, University of Newcastle, Australia
María Seron, University of NewcastleFollow
Hernan Haimovich, Universidad Nacional de RosarioFollow
Jacqueline Ramagge, University of WollongongFollow

RIS ID

25668

Publication Details

Mare, J., de Dona, J. A., Seron, M., Haimovich, H. & Ramagge, J. (2009). When does QP yield the exact solution to constrained NMPC?. International Journal of Control, 82 (5), 812-821.

Abstract

It is well known that the optimal control sequence for a linear system with a quadratic cost and linear inequality constraints over a finite optimisation horizon can be computed by means of a quadratic programme (QP). The aim of this article is to investigate when the optimal control sequence for a non-linear single-input single-output system also can be computed via QP. Our main contribution is to show that the optimal control sequence for non-linear systems, with a quadratic cost and linear inequality constraints can be computed in exact form via QP provided the optimisation horizon is no larger than a critical quantity that we name the ‘input–output linear horizon’. The results do not require any linearisation technique and are applicable to general non-linear systems, provided their input–output linear horizon is larger than their relative degree.