A novel control solution to nonlinear systems of unmatched perturbations with unknown bounds

In this study, a novel control design of nonlinear systems has been presented to solve the problem of matched and unmatched perturbations (disturbances) with unknown upper bounds. The proposed controller combined a backstepping control approach with a barrier function integral sliding mode controller (BS-BFISMC). The control design utilized the powerful backstepping control algorithm to decompose the nonlinear system into subsystems to provide global stability, while the barrier function ISMC has been adopted to cope with perturbation, avoid the pre-knowledge of upper bound in the perturbation, and mitigate the chattering effect in the control signal. A stability analysis based on Lyapunov has been conducted for the proposed BS-BFISMC to prove the ultimate boundedness of tracking errors. Another control scheme, which is concerned with the problem of unmatched perturbation, has been also presented: a robust continuous backstepping-based controller (CRBS). A comparison study has been made between the proposed BS-BFISMC and three control structures (conventional backstepping, SMC, and CRBS). Numerical simulation based on MATLAB programing software has been conducted to verify the effectiveness of the proposed control approach for a nonlinear system subjected to both matched and unmatched non-vanishing disturbance and parametric uncertainty. The performance and robustness characteristics of the proposed control scheme and other controllers have been evaluated and compared in a quantitative manner.