Computational-Physical State Co-regulation in Cyber-Physical Systems

From the perspective of physical system feedback control, the cyber or computer system's role has been to sample and compute control inputs sufficiently fast to maintain acceptable reference command tracking and disturbance rejection in the physical system. This strategy has been successful given the relatively low computational overhead for most control laws compared to computational resource availability. However, in many emerging applications this requirement may be insufficient, not because the computer is incapable of high-speed computations but instead because either more complex computations are required or because processor or network speed must be minimized to conserve energy. We propose the augmentation of traditional physical state models with a computational model to enable a cyber-physical system to co-regulate physical and computational actuation. Ultimately, our goal is to balance resources of the cyber system with quality of control of the physical system to provide a more energy-conscious CPS. As a first step, we propose a continuous-time representation of computational state and derive a continuous "dynamics" model approximation. Next, we propose the addition of a computational state into the closed-loop control law for the physical system states. Finally, we augment the derived cyber model with a second-order oscillator and demonstrate control via a LQR controller. In our simulation results, computational state and loop execution rate and oscillator "force" are regulated closed-loop at each control cycle based both on physical and computational state reference commands and errors. Results show that both physical and cyber state can be successfully regulated with the expected degradation in tracking performance as reference computational state (control loop rate) is slowed to values near the stability threshold.