Optimal control of interacting systems with DNSS property: The case of illicit drug use

In this paper we generalize a one-dimensional optimal control problem with DNSS property to a two-dimensional optimal control problem. This is done by taking the direct product of the model with itself, i.e. we combine two similar system dynamics under a joint objective functional that is separable in both states and controls. This framework can be applied to the construction of various optimal control problems, such as optimal marketing of related products, optimal growth of separate but interacting economies, or optimal control of two related capital stocks.