This paper presents a novel approach to generating stabilizing controllers for a large class of dynamical systems using diffusion models. The core objective is to develop stabilizing control functions by identifying the closest asymptotically stable vector field relative to a predetermined manifold and adjusting the control function based on this finding. To achieve this, we employ a diffusion model trained on pairs consisting of asymptotically stable vector fields and their corresponding Lyapunov functions. Our numerical results demonstrate that this pre-trained model can achieve stabilization over previously unseen systems efficiently and rapidly, showcasing the potential of our approach in fast zero-shot control and generalizability.

翻译：本文提出了一种利用扩散模型为广泛动力学系统生成镇定控制器的新方法。核心目标是通过识别与预定流形最接近的渐近稳定向量场，并据此调整控制函数来构建镇定控制函数。为此，我们采用在渐近稳定向量场及其对应李雅普诺夫函数对上进行训练的扩散模型。数值结果表明，该预训练模型能够高效且快速地实现对未见系统的镇定，展示了本方法在快速零样本控制及泛化能力方面的潜力。