Estimation of the upper bound horizon for input constrained MPC based on reachable sets

Based on the reachable sets, two new effective and less conservative algorithms for computing the upper bound of the control horizon for the input constrained model predictive control problem are presented. Reachable sets of the current state are used to predict the evolution and the minimal cost of each step from the current state. The K-step null-controllable set is used to determine which set the initial state belongs to. Then the state can reach the origin after K steps at least. The minimal cost within the reachable set is applied to compute the upper bound for an initial state. The state within the polytope can be expressed as a convex combination of the vertices of the polytope, which is used to deduce a global upper bound by solving a linear programming problem quickly. The proposed algorithms are compared with the others by an example.