Robust Backstepping Sliding Mode Control of a Class of Uncertain MIMO Nonlinear Systems

In this paper, a robust backstepping sliding mode controller is proposed for the output tracking control of a class of uncertain MIMO nonlinear systems. This controller combines the backstepping and sliding mode control, and the tracking error of the system is ultimately bounded. The recursive nature of this approach is similar to the standard backstepping, and the difference is that we use backstepping to design virtual controller including a zero-order sliding mode at each recursive step. The benefit of this approach is that each virtual controller can compensate for unknown bounded functions which represent unmodelled dynamics and disturbances. Stability analysis results are discussed, which show that the closed-loop system is ultimately bounded. Finally, we establish the reduced model of a class of nonholonomic mobile manipulators, and use the method in the output tracking control of the nonholonomic mobile manipulators. Numerical simulations are also presented to demonstrate the effectiveness of the proposed approach.