Gradient projection based algorithm for large scale real time model predictive control

In model predictive control (MPC), the quadratic program (QP) is solved at each sampling time, thus a fast and effective on-line solver must be used for short sampling times. The multi-parametric quadratic programming (mp-QP) (explicit solution) is impossible to use for larger systems due to the memory limitation. The objective of this paper is to present an effective on-line solver for large-scale simple constrained quadratic programming which arises in the MPC framework. The presented algorithm uses the combination of gradient and Newton projection method to obtain super-linear convergent algorithm which is very close to optimum in very few iterations when many constraints are active in optimum and it does not involve the exact computation of the Newton step at each iteration.