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arXiv 2302.02529eess.SYcs.LGcs.ROcs.SY
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从数据中学习面向控制的动态结构

Learning Control-Oriented Dynamical Structure from Data

Stanford University(斯坦福大学);Massachusetts Institute of Technology(麻省理工学院)

Spencer M. Richards, Jean-Jacques Slotine, Navid Azizan, Marco Pavone

AI总结:

本文针对一般非线性控制仿射系统,提出了一种基于状态依赖Riccati方程的非线性跟踪控制器,通过从有限数据中学习向量场系统的非线性分解来构建稳定闭环系统,实验证明其在轨迹跟踪中优于联合学习方法。

摘要:

即使对于已知的非线性动态系统,反馈控制器综合也是一个困难的问题,通常需要利用动态系统的特定结构来构建稳定的闭环系统。对于一般的非线性模型,包括拟合数据的模型,可能没有足够的已知结构来可靠地综合出稳定的反馈控制器。本文讨论了一种基于状态依赖 Riccati 方程的一般非线性控制仿射系统的状态依赖非线性跟踪控制器形式。该形式依赖于定义控制仿射动态的向量场系统的非线性分解,在温和的平滑性假设下该分解总是存在的。我们提出了一种从有限数据集中学习这种分解的方法。在各种模拟非线性动态系统上,我们实证证明了该控制器学习版本在稳定轨迹跟踪中的有效性。除了我们的学习方法外,我们还评估了联合学习已知动态系统的控制器和可稳定性证书的近期想法;实验表明此类方法相比之下可能较为脆弱。

英文摘要:

Even for known nonlinear dynamical systems, feedback controller synthesis is a difficult problem that often requires leveraging the particular structure of the dynamics to induce a stable closed-loop system. For general nonlinear models, including those fit to data, there may not be enough known structure to reliably synthesize a stabilizing feedback controller. In this paper, we discuss a state-dependent nonlinear tracking controller formulation based on a state-dependent Riccati equation for general nonlinear control-affine systems. This formulation depends on a nonlinear factorization of the system of vector fields defining the control-affine dynamics, which always exists under mild smoothness assumptions. We propose a method for learning this factorization from a finite set of data. On a variety of simulated nonlinear dynamical systems, we empirically demonstrate the efficacy of learned versions of this controller in stable trajectory tracking. Alongside our learning method, we evaluate recent ideas in jointly learning a controller and stabilizability certificate for known dynamical systems; we show experimentally that such methods can be frail in comparison.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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