Reference governors and maximal output admissible sets for linear periodic systems

ABSTRACT

In this paper, we consider the problem of constraint management in Linear Periodic (LP) systems using Reference Governors (RG). First, we introduce the periodic-invariant maximal output admissible sets for LP systems. We extend the earlier results in the literature to Lyapunov stable LP systems with output constraints, which arise in RG applications. We show that, while the invariant sets for these systems may not be finitely determined, a finitely-determined inner approximation, which is periodically invariant, can be obtained by constraint tightening. We then analyze the geometric and algebraic relationship between these sets and show that these sets are related via simple transformations, implying that it suffices to compute only one of them for real-time applications. This greatly reduces the memory burden of RG (or other similar constraint management strategies), at the expense of an increase in processing requirements. We present a thorough analysis of this trade-off. In the second part of this paper, we present two RG formulations, and discuss their properties and algorithms for their computation. Numerical simulations demonstrate the efficacy of the approach.

KEYWORDS:

• Constrained systems
• linear periodic systems
• predictive control
• reference governors
• invariant sets
• maximal output admissible sets

Acknowledgements

The authors greatly appreciate the valuable discussions with Dr. Mads Almassalkhi, Dr. Uroš Kalabić, and Dr. Ilya Kolmanovsky. Comments and suggestions by anonymous reviewers are also greatly appreciated.

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

H. R. Ossareh  http://orcid.org/0000-0002-4964-569X

Notes

1. Plots are generated by MPT 3.0 Toolbox in Matlab (Herceg, Kvasnica, Jones, & Morari, 2013).