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In this paper, we present physics-informed neural networks (PINNs) for the analysis and control of nonlinear systems. PINNs are designed to solve partial differential equations (PDEs). We demonstrate their applications in various challenging computational tasks in systems and control, including computing Lyapunov functions, regions of attraction, and optimal value functions and controllers for nonlinear systems. Additionally, we introduce LyZNet, a tool that combines physics-informed learning with formal verification to ensure the solutions provided by PINNs meet formal guarantees. We provide theoretical results and demonstrate with numerical examples of both low- and high-dimensional nonlinear systems to showcase the effectiveness of the proposed framework.
Liu et al. (Thu,) studied this question.