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In Data Stream Management Systems (DSMSs), request handling has to meet various QoS requirements. Traditional open-loop DSMS ignores system status information and run-time history in decision making and is unable to achieve stable QoS performance over run-time as the workload or environment changes. This paper discusses the design of a close-loop DSMS that applies adaptive control in control theory to adapt itself to the changing environment and workloads in order to optimize the QoS performance over run-time. The proposed adaptive DSMS is built on system identification and successive approximation knowledge in control theory and uses a least square approach for parameter estimation. Experimental data shows that the proposed adaptive DSMS outperforms the traditional open-loop DSMS in overall QoS among various network conditions and workload settings.