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.

Automated summary

This article proposes a composite learning control approach with a heterogeneous estimator to address the multiple uncertainties in strict-feedback nonlinear systems. By using recorded data-based neural learning and disturbance observer, the approach learns the uncertainties including nonlinear dynamics, unknown control gain function, and time-varying disturbance. The lumped prediction error is constructed and incorporated into the update law through neural approximation and disturbance observation. The proposed approach ensures input limitation by representing the control input's asymmetric saturation nonlinearity with a smooth form model and utilizes a projection algorithm to avoid singularity problem. Rigorous stability analysis of the closed-loop system is conducted, guaranteeing the boundedness of the system tracking error. Tests on a third-order nonlinear system and an autonomous underwater vehicle (AUV) demonstrate that the proposed approach improves system tracking accuracy with expected learning performance.