Zhang, Yongjun; Zhao, Jianli; Zhang, Fei; Wang, Jing Approximate finite-time control for a class of uncertain nonlinear systems with dynamic compensation. (English) Zbl 1379.93054 Int. J. Robust Nonlinear Control 27, No. 18, 4296-4311 (2017). Summary: In this work, a new robust nonlinear feedback control method with dynamic active compensation is proposed; the active control method has been applied to an integral series of finite-time single-input single-output nonlinear system with uncertainty. In further tracking the closed-loop stability and nonlinear uncertainty, an extended state observer has been employed to solve the immeasurability and nonlinear uncertainty within a nonlinear system. A singular perturbation theory has been used to ensure the finite-time stability of the closed-loop system. Furthermore, numerical simulations show that the robust nonlinear feedback controller tracks the uncertainty in a nonlinear Duffing-type oscillator and proves the effectiveness of the approximate finite-time control strategy proposed. By using an approximate finite-time control approach with active compensation, the uncertainty in a nonlinear system could be accurately estimated and controlled. MSC: 93B52 Feedback control 93B35 Sensitivity (robustness) 93C41 Control/observation systems with incomplete information 93C10 Nonlinear systems in control theory 93C70 Time-scale analysis and singular perturbations in control/observation systems 93C15 Control/observation systems governed by ordinary differential equations Keywords:approximate finite-time stability; extended state observer; nonlinear system; uncertainty; closed-loop response PDFBibTeX XMLCite \textit{Y. Zhang} et al., Int. J. Robust Nonlinear Control 27, No. 18, 4296--4311 (2017; Zbl 1379.93054) Full Text: DOI