Robust backstepping control of robotic systems using neural networks

Neural network (NN) controllers for the robust backstepping control of robotic systems in both continuous and discrete-time are presented. Control input is selected to achieve tracking performance for unknown nonlinear systems. Tuning methods are derived for the NN based on the delta rule. Novel weight tuning algorithms for the NN are obtained that are similar to ε-modification in the case of continuous-time adaptive control. Uniform ultimate boundedness of the tracking error and the weight estimates are presented without using the persistency of excitation (PE) condition. Certainty equivalence is not used and a regression matrix is not computed. No learning phase is needed for the NN and initialization of the network weights is straightforward