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This paper is concerned with the problem of maximizing capacity utilization of the battery power source in a portable electronic system under latency and loss rate constraints. First, a detailed stochastic model of a power-managed, battery powered electronic system is presented. The model, which is based on the theories of continuous-time Markovian decision processes and stochastic networks, captures two important characteristics of today's rechargeable battery cells, i.e., the current rate-capacity characteristic and the relaxation-induced recovery. Next, the battery-aware dynamic power management problem is formulated as a policy optimization problem and solved exactly by using a linear programming approach. Experimental results show that the proposed method outperforms existing heuristic methods for battery management by as much as 17% in terms of the average energy delivered per unit weight of battery cells.