Robust Adaptive Tracking Control for Nonlinearly Parameterized High-Order Systems With Unmatched Disturbances

The output tracking problem for a class of nonlinearly parameterized high-order uncertain systems with unmatched disturbances is studied. The developed robust adaptive control scheme is based on the combination of a decoupled backstepping control method for decoupling the coupling term in each step by elegantly using the Young’s inequality and an adaptive technique with fixed
$\sigma $
-modification for ensuring the boundedness of parameter estimates. The proposed controller and adaptive laws guarantee the closed-loop signals global boundedness and output tracking error boundedness in a mean square sense. Finally, the desired control properties are verified by a numerical example and a mass-spring mechanical system, respectively.