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Both bandwidth and energy become important resource constraints when multihop wireless networks are used to transport high-data-rate traffic for a moderately long duration. In such networks, it is important to control the traffic rates to not only conform to the link capacity bounds, but also to ensure that the energy of battery-powered forwarding nodes is utilized judiciously to avoid premature exhaustion (i.e., the network lasts as long as the applications require data from the sources) without being unnecessarily conservative (i.e., ensuring that the applications derive the maximum utility possible). Unlike prior work that focuses on the instantaneous distributed optimization of such networks, we consider the more challenging question of how such optimal usage of both link capacity and node energy may be achieved over a time horizon. Our key contributions are twofold. We first show how the formalism of optimal control may be used to derive optimal resource usage strategies over a time horizon, under a variety of both deterministic and statistically uncertain variations in various parameters, such as the duration for which individual applications are active or the time-varying recharge characteristics of renewable energy sources (e.g., solar cell batteries). In parallel, we also demonstrate that these optimal adaptations can be embedded, with acceptably low signaling overhead, into a distributed, utility-based rate adaptation protocol. Simulation studies, based on a combination of synthetic and real data traces, validate the close-to-optimal performance characteristics of these practically realizable protocols.