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中文摘要：
对具有非匹配不确定的高阶非线性系统,采用改进的高阶滑模微分器获取已知状态的任意阶微分估计值,再以恰当阶次的状态微分估计值之差,得到非匹配不确定项及其微分的估计值,证明了其误差任意小.为避免奇异性和抖振,采用两种方案设计了滑模控制器,并设计鲁棒项提高系统鲁棒性.基于Lyapunov理论证明了系统稳定性.同现有其他方法相比,该方法具有适用范围更广、收敛速度快、控制精度高、运算量小、保守性低等优点.最后仿真证明了本文所有结论.
英文摘要：
For higher order nonlinear system with mismatched uncertainties, we propose a new higher order sliding- mode 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.
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