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Adaptive Robust Control Based on Moore-Penrose Generalized Inverse for Underactuated Mechanical Systems

To address the uncertainty existing in underactuated mechanical systems (UMSs) and their nonholonomic servo constraints, we propose a class of adaptive robust control based on the Moore-Penrose generalized inverse for UMSs in this paper. The uncertainty is considered as (possible fast) time-varying and bounded. However, the bound is unknown. To estimate the bound information, an adaptive law is designed, which combines leakage type and dead-zone type. This adaptive law can simultaneously regulate the control effort and computation speed. The proposed control can guarantee deterministic system performance, which is analyzed by using Lyapunov method. The effectiveness of proposed control is shown by an example of simplified two-wheeled self-balancing robot.