Adaptive-Adaptive Robust (A2R) Control for Uncertain Mechanical Systems: Rendering β-Ultimate Boundedness

Abstract

A novel control scheme, namely adaptive-adaptive robust (A2R) control is proposed for motion control of mechanical systems. The system contains uncertainty which is bounded while the bound may be unknown. Two designs of robust controls are proposed, with the first class featuring leakage type and the second class featuring dead-zone type. Each class involves an adaptive law with the intension of mimicking the uncertainty bound. However, there exists an undetermined design parameter in the adaptive law. An upper-layer adaptive law for the determination of this design parameter is then proposed; hence rendering the adaptive-adaptive robust (A2R) control. The control guarantees uniform boundedness and uniform ultimate boundedness of a resulting augmented system state, including a β-measure which reflects how close the constraint is followed.