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

• 成果类型: Article
• 署名作者: Huang, Bowen; Vaidya, Umesh
• 署名单位: Clemson University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3164986
• 发表日期: 2022
• 页码: 4778-4785
• 关键词: Optimal control; Markov processes; Heuristic algorithms; control systems; Approximation algorithms; Stability criteria; Numerical stability; Convex Optimization; Data-driven control; linear operator approach

摘要

This article 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 (OCP) 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 OCP 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.