用于非线性系统的Koopman-Luenberger观测器设计及其在潜热储能系统监测中的应用
KOOPMAN-Luenberger Observer Design for Nonlinear Systems with Application to the Monitoring of a Latent Thermal Energy Storage
浏览论文内容
中文总结 AI 辅助
本研究提出KOOPMAN-LSO设计框架，结合Koopman提升与线性观测器优势，在LTES系统上实现了受限感知下的非线性状态高精度估计，验证了其实际应用潜力。
中文摘要 AI 辅助
非线性动力学系统的状态估计仍是一项基础性挑战，尤其在测量值稀疏且内部状态不可达的情况下。本研究提出一种基于Koopman的线性状态观测器（KOOPMAN-LSO）设计框架，该框架可通过Koopman算子理论为非线性系统实现线性观测器综合。利用物理信息基函数将非线性动力学提升至高维可观测空间，在该空间中通过带控制的扩展动态模态分解（eDMDc）识别带控制的线性预测器。随后在提升空间中构建离散时间Luenberger观测器，并通过对偶线性二次调节器（LQR）公式获取观测器增益，以确保估计误差动态稳定且可调。所提框架结合了Koopman提升的表征能力与线性观测器设计的简洁性及计算效率，为感知受限场景下的非线性状态估计提供了系统性方法。其有效性在基于相变材料（PCM）的潜热储能（LTES）系统上得到验证，该系统的内部温度状态无法直接测量。在不同运行条件下的实验结果表明，可从有限的输出测量值中准确重构未测量状态，证明了KOOPMAN-LSO设计在实际非线性系统中的应用潜力。该方法实现了高保真重构，LTES出口温度的均方根误差（RMSE）低至0.0819°C，可观测的内部PCM温度的RMSE普遍低于1.0°C。
英文摘要
State estimation for nonlinear dynamical systems remains a fundamental challenge, particularly when measurements are sparse and internal states are inaccessible. This work presents a KOOPMAN-based Linear State Observer (KOOPMAN-LSO) design framework that enables linear observer synthesis for nonlinear systems through KOOPMAN operator theory. The nonlinear dynamics are lifted into a higher-dimensional observable space using physics-informed basis functions, where a linear predictor with control is identified via extended dynamic mode decomposition with control (eDMDc). A discrete-time Luenberger observer is then constructed in the lifted space, and the observer gain is obtained through a dual linear - quadratic regulator (LQR) formulation to ensure stable and tunable estimation error dynamics. The proposed framework combines the representational capability of KOOPMAN lifting with the simplicity and computational efficiency of linear observer design, providing a systematic approach for nonlinear state estimation under limited sensing. Its effectiveness is demonstrated on a latent thermal energy storage (LTES) system based on phase-change materials (PCM), where internal temperature states are not directly measurable. Experimental results under varying operating conditions show accurate reconstruction of unmeasured states from limited output measurements, illustrating the potential of KOOPMAN-LSO design for practical nonlinear systems. The proposed approach achieves high-fidelity reconstruction with an RMSE as low as 0.0819 °C for the LTES outlet temperature and generally below 1.0 °C for observable internal PCM temperatures.
