Neural network prescribed-time observer-based output-feedback control for uncertain pure-feedback nonlinear systems

To prevent the complicated backstepping design, as well as the coupled design of state observer/disturbance approximator and baseline controller that makes the parameter synthesis difficult, this article proposes a neural network (NN) prescribed-time observer-based output-feedback control approach for uncertain pure- feedback nonlinear systems. After reformulating the original system into a canonical form with matched lumped disturbance, an adaptive NN prescribed-time observer (NNPTO) is developed to quickly provide accurate estimates of unknown states and disturbance. Then the observer is integrated with designed non-backstepping state-feedback controller to construct an output-feedback control scheme. Three features distinguish our approach from existing non-backstepping methods: (1) the accurate estimation is realized in a finite time prescribed through a single parameter; (2) the design of the state observer/disturbance approximator and baseline controller is decoupled, which eases the synthesis process and makes lots of existing non-backstepping state-feedback controllers compatible with our output-feedback control approach; (3) The NNPTO has trivial oscillation and small observation peaking errors under large disturbance, which effectively improves the output tracking performance. Numerical examples and an application example of a rigid single-link manipulator system are presented to demonstrate the effectiveness and practicability of our approach.