Simulation Relations for Abstraction-based Robust Control of Hybrid Dynamical Systems

Abstract

The paper addresses the problem of robust control of hybrid dynamical systems with respect to linear-time properties. First, three notions of robust controllers are formulated, that capture imperfect measurements, actuation errors and delays, and uncertain dynamics, respectively. Under mild assumptions of uniform continuity on the transition relation, robust controller synthesis problem with respect to uncertain dynamics is shown to be more general than those with respect to measurement errors, actuation errors and delays. Hence, the paper focuses on the latter notion of robust controllers. Next, foundations for abstraction-based robust controller synthesis are explored, and uniformly continuous alternating simulation relations are shown to preserve the existence of robust controllers with respect to uncertain dynamics.