Admissible sets for slowly-varying discrete-time systems

摘要

This note describes a method to calculate admissible sets for dynamical systems with slowly-varying parameters. A set of initial states is said to be admissible if all state trajectories starting within this set respect safety-critical constraints for all future time instances. For many classes of systems, the Maximal Admissible Set (MAS) equals the Maximal Robust Positive Invariant (MRPI) set. Therefore, much of the literature focus on algorithms that produce (approximations of) the MRPI set. However, for slowly-varying systems it turns out that the MAS can be larger than the MRPI set. A property referred to as the M-proximal contraction property is defined for such systems to state sufficient conditions for sets to be admissible. It is then shown that Algorithm 2 produces an admissible set that is a superset of the MRPI set. (C) 2019 Elsevier Ltd. All rights reserved.