Controlling continuous-time dynamical systems is generally a two step process: first, identify or model the system dynamics with differential equations, then, minimize the control objectives to achieve optimal control function and optimal state trajectories. However, any inaccuracy in dynamics modeling will lead to sub-optimality in the resulting control function. To address this, we propose a neural ODE based method for controlling unknown dynamical systems, denoted as Neural Control (NC), which combines dynamics identification and optimal control learning using a coupled neural ODE. Through an intriguing interplay between the two neural networks in coupled neural ODE structure, our model concurrently learns system dynamics as well as optimal controls that guides towards target states. Our experiments demonstrate the effectiveness of our model for learning optimal control of unknown dynamical systems. Codes available at https://github.com/chichengmessi/neural_ode_control/tree/main

翻译：控制连续时间动力系统通常分为两步：首先通过微分方程辨识或建模系统动力学，然后最小化控制目标以获得最优控制函数和最优状态轨迹。然而，动力学建模中的任何不精确性都会导致所得控制函数的次优性。为解决这一问题，我们提出一种基于神经ODE的未知动力系统控制方法，称为神经控制（NC），该方法通过耦合神经ODE将动力学辨识与最优控制学习相结合。通过耦合神经ODE结构中两个神经网络之间的有趣交互，我们的模型能够同时学习系统动力学以及引导系统达到目标状态的最优控制。实验证明了我们的模型在学习未知动力系统最优控制方面的有效性。代码可在 https://github.com/chichengmessi/neural_ode_control/tree/main 获取。