We consider a many-to-one sensor network where a large number of sensors are deployed to monitor a physical environment. We explore sensor activity management to maximize the network lifetime while meeting the quality of service (QoS) requirement. Specifically, in each round the sink estimates the number of active sensors and the control information is fed back to the sensors for activity control. We start with a basic case where the total number of sensors N is known, and the estimator of the number of active sensors n̂t is accurate. We devise a sensor activity control scheme under which the number of active sensors would converge to the minimum that can meet the QoS requirement. Next, we generalize the study to the following two more complicated cases: (1) The case with known N and inaccurate n̂t: For this case, we propose a stochastic approximation algorithm to minimize the average number of active sensors while meeting the QoS requirement. (2) The case with unknown N and accurate n̂t: For this case, we cast the problem as the adaptive control of a Markov chain with unknown parameters and propose a composite optimization-oriented approach for the corresponding sensor activity control. We show that using this composite optimization-oriented approach the number of active sensors would converge to the minimum that can meet the QoS requirement.