Controlling complex dynamical systems is generally associated with minimizing certain control objectives with known dynamics under the variational calculus framework. For systems with unknown dynamics, an additional step of dynamics modeling is required. However, any inaccuracy in dynamics modeling will lead to sub-optimality in the resulting control function. Another set of approaches for controlling unknown dynamical systems - reinforcement learning, folds the dynamics modeling into controller training via value function approximation or policy gradient through extensively interacting with the environment, but it suffers from low data efficiency. To address these, we introduce NODEC, a novel framework for controlling unknown dynamical systems, which combines dynamics modelling and controller training using a coupled neural ODE model. Through an intriguing interplay between the two coupled neural networks, NODEC learns system dynamics as well as optimal controls that guides the unknown dynamical system towards target states. Our experiments demonstrate the effectiveness and data efficiency of NODEC for learning optimal control of unknown dynamical systems.

翻译：控制复杂动力系统通常需要在变分法框架下，针对已知动力学过程最小化特定控制目标。对于未知动力系统，需额外进行动力学建模步骤。然而，动力学建模的任何误差都将导致控制函数的最优性下降。另一类控制未知动力系统的方法——强化学习，通过值函数近似或策略梯度与环境大量交互，将动力学建模融入控制器训练，但存在数据效率低的问题。为此，我们提出NODEC这一面向未知动力系统控制的新型框架，通过耦合神经ODE模型融合动力学建模与控制器训练。两个耦合神经网络间存在精妙交互作用，使NODEC既能学习系统动力学，又能学习引导未知动力系统趋向目标状态的最优控制策略。实验表明，NODEC在学习未知动力系统最优控制时兼具有效性与数据高效性。