Interpolation techniques in robust constrained model predictive control

Abstract

This work investigates interpolation techniques that can be employed on off-line robust constrained model predictive control for a discrete time-varying system. A sequence of feedback gains is determined by solving off-line a series of optimal control optimization problems. A sequence of nested corresponding robustly positive invariant set, which is either ellipsoidal or polyhedral set, is then constructed. At each sampling time, the smallest invariant set containing the current state is determined. If the current invariant set is the innermost set, the pre-computed gain associated with the innermost set is applied. If otherwise, a feedback gain is variable and determined by a linear interpolation of the pre-computed gains. The proposed algorithms are illustrated with case studies of a two-tank system. The simulation results showed that the proposed interpolation techniques significantly improve control performance of off-line robust model predictive control without much sacrificing on-line computational performance.