On the optimal control problem for a class of monotone bilinear systems

We consider a class of positive systems in which the control signal enters bilinearly with the state. Such dynamics arise naturally, for example, from modeling the evolutionary dynamics of HIV in the presence of drug therapy. For this class of system, we formulate an infinite horizon optimal control problem and show that the optimal control signal is constant over time. We further extend our results to the case of uncertain dynamics and provide a characterization of the optimal robust controller.