摘要：AbstractThis paper proposes a method of approximating positively invariant sets and n-step controllable sets of uncertain linear systems that are subject to chance constraints. The computed sets are robustly invariant and are guaranteed to satisfy the probabilistic constraints of the control problem. In contrast, existing methods based on random sampling are only able to satisfy such constraints with a fixed level of confidence. The proposed approach uses explicitly parametrised auxiliary disturbance sets, which are optimised subject to a constraint on their probability measure so as to maximise the relevant positively invariant or n-step controllable set. The results are illustrated by numerical examples.
