Designing Luenberger observers for nonlinear systems involves the challenging task of transforming the state to an alternate coordinate system, possibly of higher dimensions, where the system is asymptotically stable and linear up to output injection. The observer then estimates the system's state in the original coordinates by inverting the transformation map. However, finding a suitable injective transformation whose inverse can be derived remains a primary challenge for general nonlinear systems. We propose a novel approach that uses supervised physics-informed neural networks to approximate both the transformation and its inverse. Our method exhibits superior generalization capabilities to contemporary methods and demonstrates robustness to both neural network's approximation errors and system uncertainties.

翻译：设计非线性系统的Luenberger观测器涉及一项具有挑战性的任务：将状态变换到另一个坐标系（可能具有更高维度），在该坐标系中系统渐近稳定且线性化直至输出注入。观测器随后通过反演变换映射来估计原始坐标系中的系统状态。然而，对于一般非线性系统，寻找可推导逆映射的合适单射变换仍是主要难题。我们提出一种新方法，利用受物理信息驱动的监督神经网络来同时逼近变换及其逆映射。该方法相比现有方法展现出更优的泛化能力，并且对神经网络的近似误差和系统不确定性均具有鲁棒性。