Hierarchical Control for Continuous-time Systems via General Approximate Alternating Simulation Relations

TL;DR

This paper proposes a new approximate simulation relation for continuous-time systems, enabling hierarchical control with larger model mismatches, and demonstrates its effectiveness through case studies.

Contribution

It introduces the psilon-gAAS relation for continuous-time systems and develops a control refinement method for hierarchical control based on this relation.

Findings

The psilon-gAAS relation effectively relaxes existing simulation constraints.

The control refinement method enables hierarchical control for complex systems.

Case studies validate the approach's advantages over previous methods.

Abstract

This paper introduces a general approximate alternating simulation relation (\emph{$\varepsilon$-gAAS relation}) for continuous-time systems, which relaxes existing simulation relations to tolerate larger mismatches between abstract and concrete models. The definition of gAAS for continuous-time systems is first proposed, and its properties are investigated. Then, a control refinement method is developed to enable hierarchical control for the gAAS relation. Finally, case studies demonstrate the effectiveness of the proposed approach, highlighting its advantages over existing methods.