New formulation of robust MPC by incorporating off-line approach with on-line optimization

Abstract

This article addresses robust model predictive control (MPC) for systems with polytopic description. An existing off-line robust MPC enables the on-line computation as simple as searching a state feedback gain among the look-up table. We consider enlarging the region of attraction of the off-line MPC by incorporating free perturbation items. First, a larger ellipsoidal region of attraction is off-line constructed, in which a simple optimization problem is solved on-line. Then, outside of this larger ellipsoid, a standard robust MPC is solved on-line such that the overall region of attraction can be rendered as a much larger nonellipsoidal one. The proposed approach possesses all the merits of the off-line MPC and greatly enlarges the region of attraction. A simulation example is given to demonstrate the effectiveness.

Keywords:

• Robust model predictive control
• Off-line model predictive control
• Region of attraction
• Free perturbation item
• Vertex perturbation item

Acknowledgments

This work is supported by National Science and Engineering Research Council of Canada, National Nature Science Foundation of China (Grant no. 60504013) and Foundation from Educational Office of Hebei Province in China (Grant no. ZH2006008). The authors also greatly appreciate the constructive suggestions from the anonymous reviewers.