Rigorous determination of maximum controlled invariant feasible sets

Controlled invariant terminal constraints fail to enforce strong feasibility in a rich class of MPC problems, for example when employing move-blocking. In previous work, controlled invariant feasibility was proposed for the purpose of formulating strongly feasible move-blocking MPC problems. In this paper, first, a maximum controlled invariant feasible set condition is derived. Based on this condition an algorithm for rigorously under-approximating the maximum controlled invariant feasible set is presented for situations when the exact maximum controlled invariant feasible set cannot be determined. The algorithm provides an error bound and is guaranteed to terminate in a finite number of steps. Controlled invariant feasible sets are a generalization of usual controlled invariant sets. Thus the presented method can be used to determine usual controlled invariant sets also. Next, by considering a special class of move-blocking parameterization it is shown that enforcing strong feasibility via controlled invariant feasible constraints is a generalization, not specialization, of the well-known controlled invariant terminal constraint approach.