Reference Governors and Maximal Output Admissible Sets for Linear Periodic Systems

TL;DR

This paper develops methods for managing constraints in Linear Periodic systems using Reference Governors, introducing finitely-determined invariant sets and analyzing trade-offs between computational complexity and memory in real-time applications.

Contribution

It extends maximal output admissible sets to Lyapunov stable LP systems, proposes constraint tightening for finite determination, and compares two RG formulations with algorithms and simulations.

Findings

Finitely-determined invariant sets can be obtained via constraint tightening.

Transformations relate different invariant sets, simplifying computations.

Numerical simulations confirm the effectiveness of the proposed methods.

Abstract

In this paper, we consider the problem of constraint management in Linear Periodic (LP) systems using Reference Governors (RG). First, we present 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 can be obtained by constraint tightening. We further 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, 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 discuss two RG formulations and discuss their feasibility criteria and algorithms for their computation. Numerical simulations demonstrate the efficacy of the approach.