Neuro-adaptive sliding-mode control with multi-function for nonlinear systems

There are two main problems for the successful implementation of identification-based neural network control. One is the neural networks suffering from the problem of slow learning as the number of connection weights increases. Another kernel is that the mismatch between the neural network model and the controlled system always exists. To cope with the first problem, a dynamic structure of a neural network using a minimal number of basis functions (or connection weights) is employed to approximate the nonlinear function up to the required level of accuracy. In addition, a learning law with correction-term and dead-zone ensures the boundedness of the estimated connection weight without the requirement of persistent excitation for basis functions and avoids the oscillatory response of the connection weight as it is in the vicinity of its optimal value. To deal with the second kernel problem, a robust sliding-mode control with time-varying switching gain and boundary layer is proposed to improve the performances including tracking accuracy and smoothness of control input. The stability of the overall system is verified by the Lyapunov stability criterion