A neuro-adaptive variable structure control for partially unknown nonlinear dynamic systems and its application

If the unknown nonlinear dynamic system is not in a controllable canonical form or of relative degree one, then the derivative of the tracking error is unknown. The controller design for these systems will be complex. In this paper, an estimator for the unknown tracking error with order equivalent to relative degree, is first designed, to obtain a sliding surface and to reduce the number of unknown nonlinear functions required to learn. In this situation, the total number of connection weight in neural-networks decreases. Furthermore, two learning laws with e-modification are employed to ensure the boundedness of estimated connection weights without the requirement of persistent excitation (PE) condition. The system performance can be better than that of other control schemes required many learning functions. In addition, stability of the overall system is verified by Lyapunov theory so that ultimate bounded tracking is accomplished. Simulation and experimental results of four-bar-linkage system are presented to confirm the usefulness of the proposed control.