Safe Constraint Learning for Reference Governor Implementation in Constrained Linear Systems

An approach to safe and fast online learning of constraints for a continuous-time linear system subject to linear inequality constraints is developed, assuming that the number of constraints is known and measurements of the constraint signals are available. During the identification phase, a constant reference command input is applied for the duration of an epoch and constraint measurements are collected. Based on these measurements, the set of feasible constraint parameters is refined using set-membership learning techniques. The reference command value is selected so that it minimizes the worst-case uncertainty in the parameters after one epoch while safety is ensured through the use of appropriately defined safe sets. The characterization of safe sets is shown to reduce to a finite set of linear inequality constraints. A numerical case study is reported for the proposed algorithm.