Neural networks-based composite learning control for robotic systems with predefined time error constraints

This paper investigates the neural networks-based control problem for robotic systems with error constraints. By embedding a new predefined time performance function into an asymmetric barrier function, a predefined time constraints method is proposed with the following features: (1) it is a general approach that can handle asymmetric error constraints and can be directly applied to the predefined performance control for other high-order nonlinear systems without any changing; (2) both settling time and convergent compact set can be preassigned by the user; (3) the results are global i.e., the robot can start arbitrarily within the physical domain. By extending the regression operators with online data memory, a prediction error is constructed, by using which, a new neural networks based composite learning law is constructed to handle unknown dynamics. Compared with the traditional method such as gradient descent algorithm, sigma-modification and sigma-modification which cannot guarantee the convergence of the neural networks weights or can only force the weights to stay around preselected values, the neural networks guarantees that the weights converge to the region around the true values, in particular under a weak interval excitation (IE) condition rather than the typically stringent persistent excitation (PE) condition. The benefits and effectiveness of the proposed control are theoretically authenticated and experimentally validated.