Adaptive Actuator Backlash Compensation Scheme For Noncanonical Recurrent High‐Order Neural Networks‐based Nonlinear Systems

Most existing adaptive control schemes for uncertain nonlinear systems with unknown input backlash are developed within the Lyapunov‐based backstepping framework, which is applicable to systems in canonical form with explicitly known relative degrees. However, such schemes are not applicable to nonlinear systems in noncanonical form because of implicit relative degrees. This paper aims to develop a comprehensive solution framework for adaptive tracking control in uncertain noncanonical nonlinear systems with unknown input backlash. A novel parameterizable smoothing inverse model is proposed, and combined with recurrent high‐order neural networks to handle system uncertainties, based on which a gradient‐based adaptive control scheme is developed. The proposed control scheme is theoretically proven to guarantee signal boundedness and achieve the desired tracking performance of the closed‐loop system. Its effectiveness is demonstrated through a numerical example. Moreover, the proposed control scheme can be extended to accommodate general noncanonical nonlinear systems with unknown input backlash of arbitrary relative degree.