Offline robust model predictive control with rewinding prediction

In this paper we develop an algorithm to compute explicit robust MPC solutions for constrained MIMO systems with internal uncertainties and external disturbances. The approach is based on a rewinding prediction strategy to realize the finite horizon robust MPC regulator, which has the feature that only one-step state prediction is sufficient to realize robust MPC with an arbitrary predictive horizon. The paper defines a set of sub-optimization problems as multiple-parametric sub-quadratic programming (mp-SQP), and shows that the optimal solution to the mp-SQP problem is piece-wise affine functions of states, associated with piece objectives and state critical regions. Asymptotic closed-loop stability can be guaranteed by a terminal weighting and a terminal feedback gain; also by introducing two tuning variables, the algorithm is capable of adjusting the tradeoff between system performance and robustness