Constraint‐admissible sets for systems with soft constraints and their application in model predictive control

Constraint‐admissible sets have been widely used in the study of control systems with hard constraints. This paper proposes a generalization of the maximal constraint‐admissible set for constrained linear discrete‐time systems to the case where soft or probabilistic constraints are present. Defined in the most obvious way, the maximal probabilistic constraint‐admissible set is not invariant. An inner approximation of it is proposed which is invariant and has other nice properties. The application of this approximate set in a model predictive control framework with probabilistic constraints is discussed, including the feasibility and stability of the resulting closed‐loop system. The effectiveness of the proposed approach is illustrated via numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.