Closed-loop stabilization of nonlinear systems using Koopman Lyapunov-based model predictive control
Closed-loop stabilization of nonlinear systems using Koopman Lyapunov-based model predictive control
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DOI：
10.1109/cdc42340.2020.9304259
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发表时间：
2020-12
期刊：
影响因子：
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通讯作者：
Abhinav Narasingam;J. Kwon
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文献类型：
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作者：
Abhinav Narasingam;J. Kwon
本文研究非线性系统的稳定反馈控制设计问题。为了实现这一点，我们将Koopman算子理论与基于lyapunov的模型预测控制（LMPC）相结合。利用库普曼特征函数确定了非线性动力学的双线性表示。然后，利用基于辅助控制Lyapunov函数（CLF）的有界控制器作为约束，在库普曼特征函数空间中构造了一个预测控制器，从而表征了库普曼双线性系统的稳定性。与以往的研究不同，我们通过一个由连续可微函数实现的逆映射表明，所设计的控制器将库普曼双线性系统的稳定性转化为原始闭环系统。值得注意的是，在这项工作中提出的反馈控制设计仍然完全是数据驱动的，不需要任何原始系统的明确知识。此外，与标准LMPC相比，寻求双线性系统的CLF与原始非线性系统相比在计算上是有利的。最后通过一个算例说明了该方法的应用。
This work considers the problem of stabilizing feedback control design for nonlinear systems. To achieve this, we integrate Koopman operator theory with Lyapunov-based model predictive control (LMPC). A bilinear representation of the nonlinear dynamics is determined using Koopman eigenfunctions. Then, a predictive controller is formulated in the space of Koopman eigenfunctions using an auxiliary Control Lyapunov Function (CLF) based bounded controller as a constraint which enables the characterization of stability of the Koopman bilinear system. Unlike previous studies, we show via an inverse mapping - realized by continuously differentiable functions - that the designed controller translates the stability of the Koopman bilinear system to the original closed-loop system. Remarkably, the feedback control design proposed in this work remains completely data-driven and does not require any explicit knowledge of the original system. Moreover, in contrast to standard LMPC, seeking a CLF for the bilinear system is computationally favorable compared to the original nonlinear system. The application of the proposed method is illustrated on a numerical example.