Composite learning control of strict-feedback nonlinear system with unknown control gain function

The composite learning control with the heterogeneous estimator is proposed to deal with the multiple uncertainties of strict-feedback nonlinear systems. The article applies the recorded data-based neural learning and the disturbance observer (DOB) to learn the multiple uncertainties, including the nonlinear dynamics, the unknown control gain function (CGF), and the time-varying disturbance. The lumped prediction error is constructed and included into the update law by neural approximation and disturbance observation. Furthermore, the asymmetric saturation nonlinearity (ASN) of the control input is represented by the smooth form model to ensure the input limitation, and a projection algorithm is adopted to avoid the singularity problem. The closed-loop system stability is rigorously analyzed and the boundedness of the system tracking error is guaranteed. Through the tests of the third-order nonlinear system and the autonomous underwater vehicle (AUV), it is observed that the proposed approach can improve the system tracking accuracy with the expected learning performance.