A Data-Driven Formulation of the Maximal Admissible Set and the Data-Enabled Reference Governor
Hamid R. Ossareh
Abstract
The maximal admissible set (MAS) of a stable LTI system characterizes the set of all initial conditions and constant inputs for which the output satisfies pre-specified state/output constraints for all time. The MAS (or its finitely-determined, polytopic approximations) is often employed in set-theoretic methods in control and for constraint management, for example in the Reference Governor (RG) algorithm. The existing MAS (and consequently RG) formulations require a state-space model of the dynamics to characterize the MAS. In this paper, we offer an alternative, data-driven perspective: we leverage output predictors from the behavioral system theory and subspace predictive control literature to formulate a data-driven version of the MAS. As we show, the proposed set is polytopic and has finite complexity, similar to its model-based counterpart, but resides in a higher dimensional space and may have higher complexity. We present the properties of the data-driven MAS including its admissibility index, and compare the data-driven MAS against its model-based formulation, where we show that the two sets are related via a linear map under mild assumptions. Finally, we use the data-driven MAS to introduce a data-enabled RG for constraint management of closed-loop control systems. Numerical simulations are presented to illustrate the results.