A Convex Approach to Data-Driven Optimal Control via Perron–Frobenius and Koopman Operators
A Convex Approach to Data-Driven Optimal Control via Perron–Frobenius and Koopman Operators
复制标题
通过 Perron-Frobenius 和 Koopman 算子实现数据驱动最优控制的凸方法
DOI：
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发表时间：
2020
影响因子：
6.8
通讯作者：
U. Vaidya
中科院分区：
文献类型：
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作者：
Bowen Huang;U. Vaidya
本文研究了一类仿射确定性非线性系统的最优控制的数据驱动计算。我们假设控制动态系统模型不可用，并且关于系统动态的唯一信息以时间序列数据的形式可用。本文给出了非线性系统最优控制问题的一个凸形式。凸形式依赖于动力系统稳定性理论中涉及密度函数和Perron-Frobenius算子的对偶结果。我们制定的OCP作为一个无限维凸优化程序。优化问题的有限维近似依赖于Koopman算子的数据驱动计算的最新进展，这是Perron-Frobenius算子的对偶。仿真结果表明，所开发的框架的应用。
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.
DOI：
10.23919/acc50511.2021.9483245
发表时间：
2021
期刊：
American Control Conference
影响因子：
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作者：
Vaidya, Umesh;Huang, Bowen
通讯作者：
Huang, Bowen