Adaptive neural boundary control for multi-agent manipulators system with uncertainties through cooperative disturbance observers network

This paper addresses vibration control problem of multi-agent flexible manipulators systems in the presence of simultaneous uncertainty and unknown external disturbance. Particularly, the goal is to suppress vibration of both flexible link and joint angular. In this paper, the dynamic model of the considered flexible manipulator is described by the fourth order partial differential equation. Without control, the system is unstable and vibrate constantly due to initial states, the external unknown disturbances and system uncertainties. To compensate the uncertainty in each agent, the neural networks are employed and novel adaptation laws are developed to update weighting parameters in the neural networks. While for the compensation of the external disturbance a cooperative network of disturbance observers is proposed to enhance the observation reliability. With the resulting estimations of uncertainties and the unknown disturbance, adaptive distributed boundary controllers are derived to suppress vibration in-domain and keep joint angular position to zero. The closed-loop system is proven to be uniform ultimately bounded through Lyapunov stability theory. Numerical simulations result shows that compared with the proportional–derivative control, the proposed method almost reduces all overshoot and steady-state error.