论文标题
通过泰勒的扩展，数据驱动的稳定器设计和一般非线性系统的闭环分析
Data-driven stabilizer design and closed-loop analysis of general nonlinear systems via Taylor's expansion
论文作者
论文摘要
对于数据驱动的非线性系统的控制，表征动力学的基础函数通常至关重要。在现有的作品中，通常基于动力学的预知识仔细选择了基础函数，以便可以通过基础函数和实验数据来表达或良好地表达系统。对于更通用的设置，在无法获得基础功能的明确信息的情况下，本文通过Lyapunov方法介绍了稳定器设计和闭环分析的数据驱动方法。首先，基于泰勒的扩展和使用输入状态数据，稳定器和Lyapunov函数旨在使已知的局部渐近稳定稳定。然后，得出数据驱动的条件以检查给定的左旋函数函数的给定超级函数集是否是吸引区域的不变子集。主要挑战之一是如何在当地稳定器的设计中处理泰勒的其余部分以及对闭环性能的分析。
For data-driven control of nonlinear systems, the basis functions characterizing the dynamics are usually essential. In existing works, the basis functions are often carefully chosen based on pre-knowledge of the dynamics so that the system can be expressed or well-approximated by the basis functions and the experimental data. For a more general setting where explicit information on the basis functions is not available, this paper presents a data-driven approach for stabilizer design and closed-loop analysis via the Lyapunov method. First, based on Taylor's expansion and using input-state data, a stabilizer and a Lyapunov function are designed to render the known equilibrium locally asymptotically stable. Then, data-driven conditions are derived to check whether a given sublevel set of the found Lyapunov function is an invariant subset of the region of attraction. One of the main challenges is how to handle Taylor's remainder in the design of the local stabilizers and the analysis of the closed-loop performance.
