A Convex Approach to Data-driven Optimal Control via Perron-Frobenius and Koopman Operators

TL;DR

This paper introduces a convex, data-driven method for optimal control of nonlinear systems using Perron-Frobenius and Koopman operators, enabling control without explicit system models.

Contribution

It develops a novel convex formulation for optimal control based on duality between density functions and Koopman operators, applicable from time-series data.

Findings

Convex formulation for data-driven optimal control.

Finite-dimensional approximation via Koopman operator.

Simulation results validate the approach.

Abstract

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.