  In mathematical psychology, decision makers are modeled using the Lindbladian
equations from quantum mechanics to capture important human-centric features
such as order effects and violation of the sure thing principle. We consider
human-machine interaction involving a quantum decision maker (human) and a
controller (machine). Given a sequence of human decisions over time, how can
the controller dynamically provide input messages to adapt these decisions so
as to converge to a specific decision? We show via novel stochastic Lyapunov
arguments how the Lindbladian dynamics of the quantum decision maker can be
controlled to converge to a specific decision asymptotically. Our methodology
yields a useful mathematical framework for human-sensor decision making. The
stochastic Lyapunov results are also of independent interest as they generalize
recent results in the literature.
