An ad hoc computing grid is characterized not only by constraints on the available energy and communications bandwidth associated with each participating device, but also by the dynamic nature of the grid itself. This is caused by the mobile nature of the assets connected to the grid (computing devices, sensors, and users), plus the fragility of interconnecting communication links. The challenge, therefore, is to efficiently and robustly manage both computational and communication resources in this dynamic, unpredictable environment. This paper reports on one potential solution that combines Lagrangian techniques with the receding horizon concept used in modern robust control systems.