Adaptive control for a class of underactuated systems with mismatched uncertainties

An adaptive multiple-surface sliding controller (AMSSC) based on function approximation techniques (FAT) is proposed for underactuated mechanical systems with disturbances and mismatched uncertainties. The Olfati transformation is applied firstly to represent the system into a special cascade form. Some of the terms in the system dynamic equation represented in the new space might become too complex to derive, they are proposed to be regarded as uncertainties. Most conventional robust or adaptive designs fail to stabilize the closed loop dynamics. We design the AMSSC so that the system mismatched uncertainties can be properly compensated. Experimental results shows that the proposed algorithm is able to give good performance regardless of the uncertainties and time-varying parameters with two cases of an inverted pendulum and a TORA system are presented.