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This brief presents an adaptive neural zeta-backstepping control strategy for a class of uncertain nonlinear systems, which allows these systems to be practically stabilized with predefined damping ratios. By introducing the zeta-backstepping technique, system damping ratios can be predetermined based on specific parameter selection rules. To reduce the impact of unknown nonlinearities, neural networks (NNs) with gradient descent training are applied to compensate such nonlinearities online. A new filter, called dynamic command filter, is used to construct the gradient of the NNs. By resorting to second-order Lyapunov stability criteria, it is proved that the closed-loop system is practically stable and has predefined damping ratio. Finally, experiments on a perturbed direct current (DC) motor system demonstrate the advantages of the proposed method.
Zheng et al. (Fri,) studied this question.