Disturbance and delay robustness of gradient feedback systems based on static noncooperative games with application to PEV charging

This paper considers interconnected dynamical systems derived from static noncooperative games. Designing such a gradient-type feedback aims at robustly driving state variables to the vicinities of Nash equilibria in the presence of uncertainty and variation. A recently-developed small-gain framework for integral input-to-state stable systems is employed to investigate global robustness of the gradient-type dynamical system with respect to disturbances and time-delays. Stability and robustness criteria are presented, and Lyapunov-Krasovskii functionals are constructed. The developed theory is applied to the plug-in electric vehicles charging problem of allocating the charging activities to the overnight electric demand valley for reducing the impact on the electric grid. A decentralized charging scheme with guaranteed robustness is proposed. Its usefulness is illustrated by numerical simulations.