Recursive feasibility guarantees in move-blocking MPC

A method for enforcing recursive feasibility in time-invariant offset-move-blocking MPC schemes is proposed. The method constrains the state at the first prediction step to a controlled invariant feasible set, introduced recently by the authors for enforcing recursive feasibility in input-move- blocking MPC. Two algorithms for the determination of maximal controlled invariant feasible sets are presented. In the case of stabilizable, linear, time-invariant plants with time-invariant, polytopic constraints, both algorithms are semi-decidable. In situations where using one algorithm alone does not lead to decidability, both algorithms can be used together to determine a controlled invariant feasible under-approximation of the maximal controlled invariant feasible set to arbitrary accuracy.