Research Initiation Awards provide support for junior and mid-career faculty at Historically Black Colleges and Universities who are building new research programs or redirecting and rebuilding existing research programs. It is expected that the award helps to further the faculty member's research capability and effectiveness, improves research and teaching at the home institution, and involves undergraduate students in research experiences. The award to Claflin University has potential broader impacts in a number of areas. The goal of this project is to study optimal control strategy in satellite communication system to allocate power among competing user terminals, who share a frequency-selective interference channel, and would be competing for limited radio resources; as well as to enhance teaching and learning at the university by involving undergraduate students in mathematical modeling. <br/><br/>Differential game (DG) models will be used to solve for optimal control strategies, because of special features of the system – competitive and dynamical. The major components of this dynamic game are as follows: In a frequency-selective Gaussian interference channel model, there are K transmitters and K receivers in the system. Each transmitter and receiver pair will be viewed as a user or a player. The whole frequency band is divided into N frequency bins. In frequency bin f, player k allocates power in a pattern of some function, which is referred to as player k's control. With this control, if treating interference as noise, the data rate player k can achieve at time t is a function of time. Player k's objective is to maximize the data gain in a specific period of time interval, which is an integration of the data rate function over this time interval. The dynamics of the system is the rate of change of channel gain, which is a function of controls and noises. Thus, all players are combined in a same dynamic system, using their controls to realize their own data needs. Under the assumption of nonexistence of collaboration between players, a non-cooperative differential game model will be constructed to solve for optimal power allocation strategy for each player. Furthermore, cooperative and hierarchical competition models will also be studied for different types of competition. Mathematical analysis will be conducted to analyze the optimality condition of DG models. Numerical methods will be developed to solve models. The broader impacts of the project will be to directly supply satellite communication controllers with a power allocation strategy design, and to generalize solution methods developed for solving DG models and improve applicability of differential game models. This project will be conducted in collaboration with the Institute for Mathematics and its Applications at the University of Minnesota.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.