New method of sliding-mode control for higher order nonlinear system with mismatched uncertainties
非匹配不确定高阶非线性系统的滑模控制新方法

For higher order nonlinear system with mismatched uncertainties, we propose a new higher order slidingmode differentiator to obtain the arbitrary order estimates for the differential values of system states. The estimated value of mismatched disturbance and its differentiations are obtained from the differences between estimated differential values with proper orders of system states; the errors can be made arbitrary small. To avoid the singularity and chattering, we present two sliding-mode controller schemes with robust control terms to improve the system robustness. The system stability is proved by Lyapunov theorem. Compared with the existing methods, the proposed method has many advantages such as the wide application range for affine nonlinear systems, high convergence rate, high control precision, small calculation complexity, and low conservativeness, etc. Finally, simulation validates all conclusions.