We consider an uplink power control problem where each mobile wishes to maximize its throughput (which depends on the transmission powers of all mobiles) but has a constraint on the average power consumption. A finite number of power levels are available to each mobile. The decision of a mobile to select a particular power level may depend on its channel state. We consider two frameworks concerning the state information of the channels of other mobiles: (i) the case of full state information and (ii) the case of local state information. In each of the two frameworks, we consider both cooperative as well as non-cooperative power control. We manage to characterize the structure of equilibria policies and, more generally, of best-response policies in the non-cooperative case. We present an algorithm to compute equilibria policies in the case of two non-cooperative players. Finally, we study the case where a malicious mobile, which also has average power constraints, tries to jam the communication of the other mobile. Our results are illustrated and validated through various numerical examples.

The nonlinear stochastic control problem related with flow control is considered. The state of the link is described by controlled hidden Markov process while the loss flow is described by the counting process with the intensity depending on the current transmission rate and unobserved link state. The control is the transmission rate and have to be chosen as non-anticipating process depending on the observation of the loss process. The aim of the control is to achieve the maximum of some utility function taking into account the losses of transmitted information. Originally the problem belongs to a class of stochastic control with incomplete information, however, the optimal filtering equations giving the estimation of the current link state based on the observation of the loss process give the opportunity to reduce the problem to the standard stochastic control problem with full observations. Then, a necessary optimality condition is derived in the form of stochastic maximum principle which allows us to obtain explicit analytic expressions for the optimal control in some particular cases. The optimal and suboptimal controls are investigated and compared with the flow control schemes which is used in TCP/IP networks. In particular, the optimal control demonstrates a much smoother behavior than the currently used TCP/IP congestion control.