Prescribed performance control with input indicator for robot system based on spectral normalized neural networks

For a real robot system, it is not easy to use the deep neural networks to approximate the unknown nonlinear dynamics online due to limited computing resources, meanwhile the saturation of the motor also makes it difficult for the system to achieve the desired control effect. In this paper, a method combining spectral normalized deep neural networks and prescribed performance controller with saturated indicator is proposed to solve the problems of insufficient computing resources and input saturation in practical robot system control. Firstly, a low computational cost offline learning spectral normalized deep neural network with rectified linear unit activation is applied in nonlinear dynamics identification to reduce the learning computation burden. The unknown nonlinear dynamics of the robot system including Coriolis force and friction dynamics can be approximated well with good generalization ability by spectral normalized deep neural networks, and the boundedness of the approximation error can be guaranteed by the Lipschitz constraint. Subsequently, a prescribed performance controller with a saturation indicator is also introduced to improve the transient performance of the robot system and eliminate the influence of input saturation. Besides, the closed-loop stability is also proved via the Lyapunov approach. The simulation and experiment results show that the proposed method can achieve good tracking performance and better generalization capability.