Improved Function Augmented Sliding Mode Control of Uncertain Nonlinear Systems with Preassigned Settling Time

Abstract

This paper investigates the robust tracking control of second-order uncertain nonlinear systems by adopting the function augmented sliding mode control approach. An improved version of this approach is proposed such that the exact information of the initial tracking error is not required when generating the desired trajectory of the tracking error. This evidently enlarges the application scope of the function augmented sliding mode control approach. Performance functions are introduced to form the performance envelopes for the sliding mode variables. A robust sliding mode controller is constructed such that the sliding mode variables are confined within their performance envelopes. This further guarantees that the tracking error converges to the given neighbourhood of zero within the preassigned settling time provided that proper control parameters are selected. An application example on the rendezvous control of spacecraft is also employed to illustrate the effectiveness of the proposed control approach.