We introduce the framework of performative control, where the policy chosen by the controller affects the underlying dynamics of the control system.

We introduce the framework of performative control, where the policy chosen by the controller affects the underlying dynamics of the control system. We first propose a sufficient condition for the performative control problem to admit a unique PSC solution with a problem-specific structure of distributional sensitivity propagation and aggregation. We further analyze the impacts of system stability on the existence of the PSC solution. Specifically, for {almost surely strongly stable} policy-dependent dynamics, the PSC solution exists if the sum of the distributional sensitivities is small enough. We finally provide a repeated stochastic gradient descent scheme that converges to the PSC solution and analyze its non-asymptotic convergence rate.