  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
