Adaptive sliding mode control of uncertain nonlinear systems with preassigned settling time and its applications

This paper investigates the adaptive tracking control of second-order nonlinear systems with nonlinearly parameterized uncertainties and disturbances, as well as multiplicative uncertainty in the control coefficient matrix. A novel adaptive function augmented sliding mode control approach is proposed such that the tracking error converges to a neighborhood of zero with the preassigned size within the preassigned settling time. In the proposed control scheme, the control gains increase as the adaptive estimate values increase only when necessary, that is, when the current control gains are not big enough to suppress the uncertainties or disturbances; as a result, the conservativeness of control design caused by unnecessary high control gains can be effectively reduced. Moreover, the chattering phenomenon well known in the sliding mode control is eliminated by using the saturation function to replace the signum function, and the possible persistent increasing problem of the adaptive estimate values due to measurement disturbances or noises on the feedback is also well addressed by introducing “dead-zone” nonlinearities in the adaptive laws. In addition, an improved method to construct the desired error trajectory is proposed, and this method could avoid the large undershoot-like or overshoot-like phenomena, which the traditional one may result in. The obtained results are finally applied to the motion control of the underwater vehicle and the rendezvous control of spacecraft, and the simulation results illustrate the effectiveness and the advantages of the proposed control approach.