Robust adaptive sliding control for a class of MIMO nonlinear systems

Abstract

In nonlinear adaptive control, a problem arises when the identified gain matrix becomes singular. As the result the adaptive law based on the inverse dynamics of the identified model cannot be implemented. When this occurs, even if the real system is always controllable, the closed loop system becomes uncontrollable. In this paper a method for generating robust adaptive control law for MIMO systems which circumvents this problem is presented. Assuming that the gain matrix of the unknown system satisfies a certain condition, estimation of the nonlinear gain matrix is reduced to one of estimating a scalar nonzero variable. Adaptive laws are designed to turn the unknown parameters on line as unknown functions are approximated using one hidden layer network. A specific a-modification adaptive law is designed to preclude the possibility of closed-loop system instability. The resulting closed-loop system is proved to be globally stable with tracking error that converges to a small residual set.