Sliding mode control with estimated equivalent control for MIMO affine nonlinear systems

A new adaptive type sliding mode controller is presented to avoid the problem of the chattering and the excessive switching gain proportional to the upper bounds of system uncertainty in the application of sliding mode control. The proposed control is composed of linear feedback control and feedforward control which is constructed from an estimated equivalent control. The estimated equivalent control is obtained from an estimation system which uses a neural network´s most powerful ability, that is, function approximation. The reaching condition is assured by the application of Lyapunov design method. The numerical examples are shown to confirm the validity of the proposed controller.