Subliminal air traffic control: Human friendly control of a multi-agent system

We present a mathematical framework for a novel concept of computer-aided air-traffic management called subliminal control. The premise is that a large part of air traffic controllers workload is devoted to monitoring situations which are likely to become unsafe. The automated control system, using an accurate prediction model and a datalink with the aircraft, has to operate small adjustments in the speeds of aircraft early enough to prevent the perception of a risk of conflict. These actions have to be small enough to be imperceptible by air traffic controllers. We formulate the subliminal control problem as a robust optimization problem in which the cost is related to the perception of risk. We use a hybrid control model with uncertainty and state constraints, and solve the problem in a game setting by using tools from viability theory. We develop this approach on an example and provide numerical results.