We consider the questions connected with the approximation of a real continuous 1-periodic functions and give a new proof of the equivalence of the special Boman-Shapiro modulus of continuity with Peetre’s K-function...We consider the questions connected with the approximation of a real continuous 1-periodic functions and give a new proof of the equivalence of the special Boman-Shapiro modulus of continuity with Peetre’s K-functional. We also prove Jackson’s inequality for the approximation by trigonometric polynomials.展开更多
An inverse theorem for the best weighted polynomial approximation of a function in L<sub>w<sub>α</sub></sub><sup>p</sup>（S） is established. We also investigate Besov spaces gener...An inverse theorem for the best weighted polynomial approximation of a function in L<sub>w<sub>α</sub></sub><sup>p</sup>（S） is established. We also investigate Besov spaces generated by Freud weight and their connection with algebraic polynomial approximation in L<sub>p</sub>（R）w<sub>λ</sub>, where w<sub>α</sub> is a Jacobi-type weight on S, 0【p≤∞, S is a simplex and W<sub>λ</sub> is a Freud weight. For Ditzian-Totik K-functionals on L<sub>P</sub>（S）, 1≤P≤∞, we obtain a new equivalence expression.展开更多
We investigate Besov spaces and their connection with trigonometric polynomial approximation in L_p[－π,π], algebraic polynomial approximation in L_p[-1,1], algebraic polynomial approximation in L_p(S), and entir...We investigate Besov spaces and their connection with trigonometric polynomial approximation in L_p[－π,π], algebraic polynomial approximation in L_p[-1,1], algebraic polynomial approximation in L_p(S), and entire function of exponential type approximation in Lp(R), and characterize K-functionals for certain pairs of function spaces including (Lp [-π,π], B_s~α (Lp[-π，π])), (L_p(R),B_s~α (Lp(R))), (Lp[-1,1],B_s~α (Lp[-1,1])), and (Lp(S),B_s~α (Lp(S))), where 0<s<, 0<p<1, S is a simple polytope and 0<α<r.展开更多
自平衡机器人是验证各种控制算法的经典装置,研究传输时滞对其控制系统的影响具有重要意义。基于李雅普诺夫-克拉索夫斯基(Lyapunov-Krasovskii,L-K)泛函方法讨论了自平衡机器人的控制问题。首先,建立了直流电机的线性化模型,并应用拉...自平衡机器人是验证各种控制算法的经典装置,研究传输时滞对其控制系统的影响具有重要意义。基于李雅普诺夫-克拉索夫斯基(Lyapunov-Krasovskii,L-K)泛函方法讨论了自平衡机器人的控制问题。首先,建立了直流电机的线性化模型,并应用拉格朗日方程法建立了自平衡机器人的线性数学模型;然后,进一步考虑传输时滞环节,建立基于多闭环比例积分微分(proportional integral differential,PID)控制器的自平衡机器人控制系统的整体状态空间模型;最后,应用广义自由矩阵积分不等式,建立了低保守性的L-K稳定性判据,在此基础上通过MATLAB中的线性矩阵不等式(linear matrix inequality,LMI)工具箱去求解PID控制增益对时滞稳定裕度的影响。仿真结果表明,所提出的系统稳定性判据不仅有效,而且具有较低的保守性。展开更多
文摘We consider the questions connected with the approximation of a real continuous 1-periodic functions and give a new proof of the equivalence of the special Boman-Shapiro modulus of continuity with Peetre’s K-functional. We also prove Jackson’s inequality for the approximation by trigonometric polynomials.
文摘An inverse theorem for the best weighted polynomial approximation of a function in L<sub>w<sub>α</sub></sub><sup>p</sup>（S） is established. We also investigate Besov spaces generated by Freud weight and their connection with algebraic polynomial approximation in L<sub>p</sub>（R）w<sub>λ</sub>, where w<sub>α</sub> is a Jacobi-type weight on S, 0【p≤∞, S is a simplex and W<sub>λ</sub> is a Freud weight. For Ditzian-Totik K-functionals on L<sub>P</sub>（S）, 1≤P≤∞, we obtain a new equivalence expression.
基金This project is supported by the National Natural Science Foundation of China.
文摘We investigate Besov spaces and their connection with trigonometric polynomial approximation in L_p[－π,π], algebraic polynomial approximation in L_p[-1,1], algebraic polynomial approximation in L_p(S), and entire function of exponential type approximation in Lp(R), and characterize K-functionals for certain pairs of function spaces including (Lp [-π,π], B_s~α (Lp[-π，π])), (L_p(R),B_s~α (Lp(R))), (Lp[-1,1],B_s~α (Lp[-1,1])), and (Lp(S),B_s~α (Lp(S))), where 0<s<, 0<p<1, S is a simple polytope and 0<α<r.
文摘自平衡机器人是验证各种控制算法的经典装置,研究传输时滞对其控制系统的影响具有重要意义。基于李雅普诺夫-克拉索夫斯基(Lyapunov-Krasovskii,L-K)泛函方法讨论了自平衡机器人的控制问题。首先,建立了直流电机的线性化模型,并应用拉格朗日方程法建立了自平衡机器人的线性数学模型;然后,进一步考虑传输时滞环节,建立基于多闭环比例积分微分(proportional integral differential,PID)控制器的自平衡机器人控制系统的整体状态空间模型;最后,应用广义自由矩阵积分不等式,建立了低保守性的L-K稳定性判据,在此基础上通过MATLAB中的线性矩阵不等式(linear matrix inequality,LMI)工具箱去求解PID控制增益对时滞稳定裕度的影响。仿真结果表明,所提出的系统稳定性判据不仅有效,而且具有较低的保守性。
