Multi-agent stochastic control: models inspired from quantum physics

In this paper, we consider multi-agent stochastic optimization and control problems, with partial information. The agent can operate in a distributed and asynchronous fashion. We investigate new problems that arise out of the interaction between observations and control actions by the agent. We show that new non-classical and non-commutative probability models are needed in order to properly formulate such problems. The models we develop here are inspired by models developed for dynamical physics problems. We establish a series of fundamental results for the trade-off between information and control patterns in distributed stochastic control, detection and estimation.