A disturbance observer(DOB)based-backstepping sliding mode control scheme is discussed for a class of semi-strict nonlinear system with unknown parameters and mismatched uncertainty.Firstly,adaptive technique and DOB ...A disturbance observer(DOB)based-backstepping sliding mode control scheme is discussed for a class of semi-strict nonlinear system with unknown parameters and mismatched uncertainty.Firstly,adaptive technique and DOB are respectively applied to tackle the unknown parameters and mismatched uncertainty,where the DOB can effectively alleviate the chattering problem of sliding mode control(SMC).Then,exponential sliding mode surface is proposed to improve the convergence rate of the sliding mode state.The‘explosion of complexity’problem inherent in conventional backstepping control is overcome by designing the novel first-order filter.The stability of the closed-loop system is analyzed in the framework of Lyapunov stability theory,in which the tracking error converges to an arbitrarily small neighborhood around zero(ASNZ).At last,two examples are given to illustrate the effectiveness of the proposed control strategy.展开更多
In this paper we give the following main results: (ⅰ) Let F(?) and G(?) be two free modules. Then F(?) and G(?) are semi-linearly isomorphic if and only if End F(?) and End G(?) are strictly isomorphic. (ⅱ) We give ...In this paper we give the following main results: (ⅰ) Let F(?) and G(?) be two free modules. Then F(?) and G(?) are semi-linearly isomorphic if and only if End F(?) and End G(?) are strictly isomorphic. (ⅱ) We give a new method to generalize the Bolla theorem in 1985 which gave a categorical description for isomorphism between End F(?) and End G(?). (ⅲ) The Wolfson theorem is a corollary of our theorem.展开更多
基金the Natural Science Foundation of Hebei Province under Grant Nos.F2020203105,F2017203130the National Natural Science Foundation of China under Grant Nos.61503323,61673294。
文摘A disturbance observer(DOB)based-backstepping sliding mode control scheme is discussed for a class of semi-strict nonlinear system with unknown parameters and mismatched uncertainty.Firstly,adaptive technique and DOB are respectively applied to tackle the unknown parameters and mismatched uncertainty,where the DOB can effectively alleviate the chattering problem of sliding mode control(SMC).Then,exponential sliding mode surface is proposed to improve the convergence rate of the sliding mode state.The‘explosion of complexity’problem inherent in conventional backstepping control is overcome by designing the novel first-order filter.The stability of the closed-loop system is analyzed in the framework of Lyapunov stability theory,in which the tracking error converges to an arbitrarily small neighborhood around zero(ASNZ).At last,two examples are given to illustrate the effectiveness of the proposed control strategy.
文摘In this paper we give the following main results: (ⅰ) Let F(?) and G(?) be two free modules. Then F(?) and G(?) are semi-linearly isomorphic if and only if End F(?) and End G(?) are strictly isomorphic. (ⅱ) We give a new method to generalize the Bolla theorem in 1985 which gave a categorical description for isomorphism between End F(?) and End G(?). (ⅲ) The Wolfson theorem is a corollary of our theorem.
