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Computer systems hosting critical e-commerce applications must typically satisfy stringent quality-of-service (QoS) requirements under dynamic operating conditions and workloads. Also, as such systems increase in size and complexity, maintaining the desired QoS by manually tuning the numerous performance-related parameters will become very difficult. This paper addresses the design of self-optimizing computer systems using a generic online control framework in which the control actions governing the operation of the system are obtained by optimizing its behavior, as forecast by a mathematical model, over a limited time horizon. As a specific application of this control technique, we show how to minimize the power consumed by a single computer processing a time-varying workload. Assuming a processor capable of operating at multiple frequencies, we design an online controller to satisfy the QoS requirements of the workload while operating the processor at the lowest possible frequency. We describe the processor model, formulate the power management problem, and derive the online control algorithm. The performance of the controller is evaluated using representative e-commerce workloads. Finally, we discuss how the proposed technique can be applied to other resource management problems in computer systems.