Single input RBF neural robust controller design for a class of nonlinear system with linear input unmodeled dynamics and unknown control function matrices

Considered both the situation with unknown control function matrices and the situation with linear unmodeled input dynamics, single input RBF neural robust controller was designed by using adaptive backstepping method for a class of multi-input to multi-output nonlinear systems which could be turned to "standard block control type". Also the PID control was introduced to make use of the known information of the system as maximally as possible. And a new kind of tuning law of neural network was chose to improve the ability of neural network to approximate the unknown function. Also introducing of robust control compensated the reconstruction error of neural networks. It was proved by constructing Lyapunov function step by step that all signals of the system are bounded and exponentially converges to the neighborhood of the origin globally. Finally, simulation study is given to demonstrate that the proposed method is effective.