Dynamical robust backstepping using a combined sliding modes and high-gain observer approach

The design of a controller and high-gain observer methodology which aims to simplify the backstepping procedure is presented. This approach differs from standard backstepping in that the virtual control inputs are designed based on estimates of the previous virtual control inputs. This eliminates the need to take derivatives of the system dynamics, which simplifies the control law and reduces the overcompensation of uncertainty. Robustness in the design is provided by a zero-order sliding mode used at each step. The virtual control input estimates used in the control design are generated by second-order high-gain observers. The high-gain observers include a zero-order sliding mode for robustness to uncertainty resulting from a coupling between the controller and observers. Stability analysis results for the coupled controller-observer system are discussed, which show that the closed-loop system is ultimately bounded. Numerical simulations are also presented to demonstrate the effectiveness of the proposed approach.