Explicit robust model predictive control using recursive closed-loop prediction

In this paper, we develop an algorithm to compute robust MPC explicit solutions for constrained MIMO systems with internal uncertainties and external disturbances. Our approach is based on a recursive closedloop prediction strategy to realize a finite horizon robust MPC regulator, which has the feature that only one-step state prediction is sufficient to realize robust MPC with an arbitrary prediction horizon. The paper defines a set of recursive sub-optimization problems as multiple-parametric sub-quadratic programming (mp-SQP), and shows that the optimal solution to the mp-SQP problem is piecewise 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 trade-off between system performance and robustness. The state admissible set, which is not easily derived from physical vision, is constructed by two methods: a piecewise linear norm of signals, and polyhedral Voronoi sets. Finally, two simulation examples demonstrate that the algorithm is efficient, feasible and flexible, and can be applied to both slow and fast industrial MIMO systems. Copyright # 2006 John Wiley & Sons, Ltd.