Trigonometric RBF neural robust controller design for a class of nonlinear system with linear input unmodeled dynamics

Considered both the situation with unknown control function matrices and the situation with linear unmodeled input dynamics, adaptive 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”. It was proved by constructing Lyapunov function step by step that all signals of the system are bounded and exponentially converge to the neighborhood of the origin globally. And by adopting the trigonometric function as basis function, the input need not be force to between −1 and 1, and there is no need to choose the centre of basis function which reduced the difficulty of doing simulation and made the neural net work more practical. And the variable structure control is adopt to eliminate the error of approximation. Also the method of differential reconstruction of neural network is used to increase the damp of neural network and it makes the system more stable. Finally, simulation study is given to demonstrate that the proposed method is effective and the known information of system was made use of as maximally as possible by introducing the PID control.