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

Abstract

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