Self-Triggered Control to Guarantee Forward Pre-Invariance with Uniformly Positive Inter-Event Times

In this paper, we propose a self-triggered control strategy to guarantee forward pre-invariance of a closed set for a control system modeled by a constrained differential inclusion. Using a (not necessarily periodic) zero-order hold control scheme, this paper addresses two key issues: i) computing the time of the next sampling event, and ii) the assurance of a uniform lower bound on the inter-event times, both while guaranteeing forward invariance. Our results guarantee forward pre- invariance on unbounded sets. Critically, the results impose mild regularity on the right-hand side of the system and on the barrier certificates. Simulations showcase the proposed algorithms and provide comparisons with the literature.