Sliding Mode Control in Backstepping Framework for a Class of Nonlinear Systems

Abstract

Both backstepping control (BC) and sliding mode control (SMC) have been studied extensively over the past few decades, and many variations of controller designs based on them can be found in the literature. In this paper, sliding mode control in a backstepping framework (SBC) for a class of nonlinear systems is proposed and its connections to SMC studied. SMC is shown to be a special case of SBC. Without losing generality, the regulation control problem is studied, while tracking control is achieved by replacing the states with the difference between the states and their desired values. The SBCs are designed for nonlinear single-input-single-output (SISO) and multiple-input-multiple-output (MIMO) systems with the presence of bounded uncertainties from unmodeled dynamics, parametric variations, disturbances, and measurement noise, and the closed loop systems are proven to be asymptotically stable using the Lyapunov stability theory. The comparison of SBC to SMC from the design process, chattering effects, and chatter reduction are also discussed. SBC inherits the merits of backstepping control in choosing gains independently, while leveraging useful nonlinear dynamics for controller design simplification. Hence, it provides more flexibility in controller design in the sense of controlling coverage speed and making use of useful nonlinearities in the dynamics. To demonstrate the effectiveness of SBC, an application on cruise tracking control of an autonomous underwater vehicle was studied.