An optimal control problem with state space constraints arising in the design of bipolar transistors

We consider the problem of determining the optimal profile of doping concentration that minimizes the base transit time in homojunction bipolar transistors. This is a well-studied problem in the electronics literature, but typically only numerical optimization is used to find solutions. Also, we include a fixed base resistance, a constraint often ignored in numerical approaches. In this paper we give an explicit analytic solution to the problem using the Pontryagin maximum principle with state-space constraints and outline how its optimality can be proven using synthesis type arguments.