Controlled invariant feasibility - A general approach to enforcing strong feasibility in MPC applied to move-blocking

Strong feasibility of MPC problems is usually enforced by constraining the state at the final prediction step to a controlled invariant set. However, such terminal constraints fail to enforce strong feasibility in a rich class of MPC problems, for example when employing move-blocking. In this paper a generalized, least restrictive approach for enforcing strong feasibility of MPC problems is proposed and applied to move-blocking MPC. The approach hinges on the novel concept of controlled invariant feasibility. Instead of a terminal constraint, the state of an earlier prediction step is constrained to a controlled invariant feasible set. Controlled invariant feasibility is a generalization of controlled invariance. The convergence of well-known approaches for determining maximum controlled invariant sets, and j-step admissible sets, is formally proved. Thus an algorithm for rigorously approximating maximum controlled invariant feasible sets is developed for situations where the exact maximum cannot be determined.

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