论文标题
通过Perron-Frobenius和Koopman操作员通过数据驱动的最佳控制的凸方法
A Convex Approach to Data-driven Optimal Control via Perron-Frobenius and Koopman Operators
论文作者
论文摘要
本文是关于一类控制仿射确定性非线性系统的最佳控制的数据驱动计算。我们假设控制动态系统模型不可用，并且有关系统动力学的唯一信息以时间序列数据的形式可用。我们为非线性系统的最佳控制问题提供了凸公式。凸公式依赖于二元性会导致动力学系统的稳定性理论涉及密度函数和perron-frobenius操作员。我们将最佳控制问题提出为无限维凸优化程序。优化问题的有限维近似取决于Koopman操作员数据驱动计算中的最新进展，该计算对Perron-Frobenius操作员是双重的。提出了仿真结果以证明开发框架的应用。
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.
