Data-driven optimal control via linear transfer operators: A convex approach

This paper is concerned with the data-driven optimal control of nonlinear systems. We present a convex formulation problem discounted cost function. consider problems both positive and negative discount factors. The approach relies on lifting system dynamics in space densities using linear Perron–Frobenius operator. leads to an infinite-dimensional optimization problem. approximation Koopman operator its dual: operator, polynomial basis write approximate finite-dimensional as which then solved efficiently sum-of-squares-based framework. Simulation results demonstrate efficacy developed