Active learning for anti-disturbance dual control of unknown nonlinear systems

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.