Toward Continuous State–Space Regulation of Coupled Cyber–Physical Systems

Cyber-physical system (CPS) research aims to integrate physical and computational models in a manner that outperforms a system in which the two models are kept separate. CPSs can be generated by either folding properties of the physics-based system into a discrete modeling paradigm or vice versa. This paper studies the latter by abstracting execution rate of a real-time feedback control task into a continuous state-space form traditionally employed for physics-based systems. We propose coupling the two models in a linear systems framework and study the impact of this coupling applied to a single degree of freedom second-order oscillator as well as an unstable inverted pendulum, both regulated with an appropriately designed linear quadratic regulator (LQR). Our results illustrate the utility of the proposed abstraction and controller design as a means of coregulating cyber and physical states in real time.