Reference governors and maximal output admissible sets for linear periodic systems

Abstract

ABSTRACTIn 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.