  This work concerns the control of unknown nonlinear systems corrupted by
disturbances. For such systems, we propose an anti-disturbance dual control
approach with active learning of the disturbances. Our approach holds the dual
property of handling the two tasks simultaneously and iteratively: (i) learn
the disturbances affecting the system and (ii) drive the system output towards
a reference trajectory. Particularly, we model nonlinear system dynamics using
a specialized neural network (SNN). This SNN formulates the disturbances via
the designed additive and multiplicative disturbance components. We consider
both additive and multiplicative disturbances for precise description and
recognition of disturbance profile. We achieve the disturbance recognition in
the SNN via the design of a Bayesian-based active learning approach, which
allows the disturbance learning to be decoupled from the control law
derivation. Such a decoupling contributes to the control robustness in the
existence of varying and abrupt disturbances. We derive the dual control law
based on the active learning of the SNN, and validate our approach via one-time
and Monte Carlo simulations. The results demonstrate a fast disturbance
recognition by our method in real-time and the robustness of control of unknown
systems with abrupt disturbances. We evaluate our approach on the speed control
of high-speed train, and the results manifest efficient control of the train
speed with disturbance resilience, without prior knowledge about the train
dynamics and the disturbances imposed on the train. We openly released the code
for this work for reproduction purpose.
