  The paper is about the data-driven computation of optimal control for a class
of control affine deterministic nonlinear systems. We assume that the control
dynamical system model is not available, and the only information about the
system dynamics is available in the form of time-series data. We provide a
convex formulation for the optimal control problem of the nonlinear system. The
convex formulation relies on the duality result in the dynamical system's
stability theory involving density function and Perron-Frobenius operator. We
formulate the optimal control problem as an infinite-dimensional convex
optimization program. The finite-dimensional approximation of the optimization
problem relies on the recent advances made in the Koopman operator's
data-driven computation, which is dual to the Perron-Frobenius operator.
Simulation results are presented to demonstrate the application of the
developed framework.
