Interpolation techniques for robust constrained model predictive control based on polyhedral invariant set

Abstract

© The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. This work studies interpolation techniques that can be employed on off-line robust constrained model predictive control (MPC) for a discrete time-varying system with polytopic parametric uncertainty. A sequence of feedback gains is determined by solving off-line a series of optimal control optimization problems. A sequence of nested corresponding polyhedral invariant 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. Two interpolation algorithms are investigated. The proposed algorithms are illustrated with case studies of a two-tank system and a four-tank system. The simulation results showed that the proposed interpolation techniques can improve control performance of off-line robust MPC while on-line computation is still tractable.