When does QP yield the exact solution to constrained NMPC?

JOSÉ MARE; JOSÉ DE DONÁ; MARÍA M. SERON; HERNAN HAIMOVICH; JACQUELINE RAMAGGE

INTERNATIONAL JOURNAL OF CONTROL

Taylor and Francis Ltd.

Lugar: Oxford, UK; Año: 2009 vol. 82 p. 812 - 821

0020-7179

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 nonlinear systems, provided their input–output linear horizon is larger than their relative degree.