论文标题
通过线性传输操作员数据驱动的最佳控制：凸方法
Data-Driven Optimal Control via Linear Transfer Operators: A Convex Approach
论文作者
论文摘要
本文涉及数据驱动的非线性系统的最佳控制。我们向具有折扣成本功能的最佳控制问题（OCP）提供了凸公式。我们认为OCP具有正折扣和负折扣因子。凸方法依赖于使用线性Perron-Frobenius（P-F）操作员在密度空间中提升非线性系统动力学。这种提升导致最佳控制问题的无限维凸优化公式。优化问题的数据驱动近似依赖于使用多项式基础函数的Koopman运算符的近似。我们将近似有限维优化问题写为多项式优化，然后使用基于平方的优化框架有效地求解。提出了仿真结果，以证明开发的数据驱动的最佳控制框架的功效。
This paper is concerned with data-driven optimal control of nonlinear systems. We present a convex formulation to the optimal control problem (OCP) with a discounted cost function. We consider OCP with both positive and negative discount factor. The convex approach relies on lifting nonlinear system dynamics in the space of densities using the linear Perron-Frobenius (P-F) 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 using the 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 are presented to demonstrate the efficacy of the developed data-driven optimal control framework.
