Adaptive Neural Network Command Filtered Backstepping Control for the Underactuated TORA System

An adaptive neural network command-filtered backstepping design algorithm is proposed for the underactuated translational oscillator with a rotating actuator (TORA). The system dynamics are transformed into a nonlinear cascade system through a global change of coordinates. Considering the weak sinusoid-type nonlinear interaction and affine-free appearance in the cascade model, the TORA is looked at as a pure feedback system. Two neural networks are used to approximate the unknown functions and a command filter is used to produce the virtual control and its first and second-order derivatives to overcome the explosion of complexity problems in backstepping. A filter error compensation dynamic system is designed to overcome the error influence on control performance. Taking full account of the cascade model structure of the underactuated TORA, each backstepping step is designed for a second-order subsystem to reduce the design steps and simplify the design process. The system stability is proved through the Lyapunov stability theorem and verified by numerical simulations.