Model-free tracking control of complex dynamical trajectories with
  machine learning
Zheng-Meng Zhai Mohammadamin Moradi Ling-Wei Kong Bryan Glaz Mulugeta Haile Ying-Cheng Lai
Nonlinear tracking control enabling a dynamical system to track a desired
trajectory is fundamental to robotics, serving a wide range of civil and
defense applications. In control engineering, designing tracking control
requires complete knowledge of the system model and equations. We develop a
model-free, machine-learning framework to control a two-arm robotic manipulator
using only partially observed states, where the controller is realized by
reservoir computing. Stochastic input is exploited for training, which consists
of the observed partial state vector as the first and its immediate future as
the second component so that the neural machine regards the latter as the
future state of the former. In the testing (deployment) phase, the
immediate-future component is replaced by the desired observational vector from
the reference trajectory. We demonstrate the effectiveness of the control
framework using a variety of periodic and chaotic signals, and establish its
robustness against measurement noise, disturbances, and uncertainties.