Computing Robust Controlled Invariant Sets of Linear Systems
For control engineers, this provides practical algorithms to compute invariant sets with formal guarantees, though the methods are incremental extensions of existing set-based techniques.
The paper presents two methods for computing robust controlled invariant sets of linear systems with bounded perturbations: one provides an arbitrarily precise outer approximation with small constraint violation, and the other provides an inner approximation. The outer method is δ-complete for constraints as finite unions of polytopes.
We consider controllable linear discrete-time systems with bounded perturbations and present two methods to compute robust controlled invariant sets. The first method tolerates an arbitrarily small constraint violation to compute an arbitrarily precise outer approximation of the maximal robust controlled invariant set, while the second method provides an inner approximation. The outer approximation scheme is $δ$-complete, given that the constraint sets are formulated as finite unions of polytopes.