Disturbance and Delay Robustness Guarantees of Gradient Systems Based on Static Noncooperative Games With an Application to Feedback Control for PEV Charging Load Allocation

This paper investigates robustness of gradient-type dynamical systems derived from static noncooperative games with a large number of players. The control objective is to drive state variables to the vicinities of Nash equilibria in the presence of disturbance and time-delay. The framework of integral input-to-state stability for large-scale systems is employed for verifying such global robustness. Several robustness criteria are presented, and Lyapunov-Krasovskii functionals are constructed. The developed theory is applied to the plug-in electric vehicle charging problem of allocating the charging load to the overnight demand valley to reduce the impact on the electric grid. Securing robustness of the dynamic load allocation is important, since eliminating uncertainties in demand predictions would become harder due to energy storage integration coupled with various energy-aware technologies. Introducing feedback, this paper guarantees stability and achieves robustness of the allocation dynamics subject to communication delay when demand predictions are not accurate. The usefulness of the proposed decentralized scheme is illustrated by numerical simulations.