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In this paper, we explore the feasibility and performanceoptimization problems for real-time systems that must remainfunctional during an operation/mission with a fixed, initialenergy budget. We show that the feasibility problem is NP-Hardin the context of systems with Dynamic Voltage Scaling(DVS) capability and discrete speed levels. Then, we focuson energy-constrained periodic task systems where theavailable energy budget is not sufficient to meet all thedeadlines. We propose techniques to maximize the totalnumber of deadlines met and the total reward (utility) whileguaranteeing the completion of the mission and a minimumperformance for each task. We consider separately: (i)systems with or without DVS capability, and (ii) off-line(static) and on-line (dynamic) solutions to select mostvaluable jobs for execution. We also discuss the tractabilityof the involved optimization problems. Our on-linealgorithms combine job promotion, job demotion and speedreduction techniques to maximize the system performancewhile guaranteeing the completion of the mission. Weevaluate our schemes through simulations and show that theon-line schemes can yield significant performanceimprovements over static solutions.