For a class of fractional-order linear continuous-time switched systems specified by an arbitrary switching sequence,the performance of PDα-type fractional-order iterative learning control(FOILC)is discussed in the s...For a class of fractional-order linear continuous-time switched systems specified by an arbitrary switching sequence,the performance of PDα-type fractional-order iterative learning control(FOILC)is discussed in the sense of L^p norm.When the systems are disturbed by bounded external noises,robustness of the PDα-type algorithm is firstly analyzed in the iteration domain by taking advantage of the generalized Young inequality of convolution integral.Then,convergence of the algorithm is discussed for the systems without any external noise.The results demonstrate that,under some given conditions,both convergence and robustness can be guaranteed during the entire time interval.Simulations support the correctness of the theory.展开更多
For 1≤ p 【 ∞, firstly we prove that for an arbitrary set of distinct nodes in [-1, 1], it is impossible that the errors of the Hermite-Fejr interpolation approximation in L p -norm are weakly equivalent to the corr...For 1≤ p 【 ∞, firstly we prove that for an arbitrary set of distinct nodes in [-1, 1], it is impossible that the errors of the Hermite-Fejr interpolation approximation in L p -norm are weakly equivalent to the corresponding errors of the best polynomial approximation for all continuous functions on [-1, 1]. Secondly, on the ground of probability theory, we discuss the p-average errors of Hermite-Fejr interpolation sequence based on the extended Chebyshev nodes of the second kind on the Wiener space. By our results we know that for 1≤ p 【 ∞ and 2≤ q 【 ∞, the p-average errors of Hermite-Fejr interpolation approximation sequence based on the extended Chebyshev nodes of the second kind are weakly equivalent to the p-average errors of the corresponding best polynomial approximation sequence for L q -norm approximation. In comparison with these results, we discuss the p-average errors of Hermite-Fejr interpolation approximation sequence based on the Chebyshev nodes of the second kind and the p-average errors of the well-known Bernstein polynomial approximation sequence on the Wiener space.展开更多
基金supported by the National Natural Science Foundation of China(61201323)the Special Fund Project for Promoting Scientific and Technological Innovation in Xuzhou City(KC18013)the Cultivation Project of Xuzhou Institute of Technology(XKY2017112)
文摘For a class of fractional-order linear continuous-time switched systems specified by an arbitrary switching sequence,the performance of PDα-type fractional-order iterative learning control(FOILC)is discussed in the sense of L^p norm.When the systems are disturbed by bounded external noises,robustness of the PDα-type algorithm is firstly analyzed in the iteration domain by taking advantage of the generalized Young inequality of convolution integral.Then,convergence of the algorithm is discussed for the systems without any external noise.The results demonstrate that,under some given conditions,both convergence and robustness can be guaranteed during the entire time interval.Simulations support the correctness of the theory.
基金supported by National Natural Science Foundation of China (Grant No.10471010)
文摘For 1≤ p 【 ∞, firstly we prove that for an arbitrary set of distinct nodes in [-1, 1], it is impossible that the errors of the Hermite-Fejr interpolation approximation in L p -norm are weakly equivalent to the corresponding errors of the best polynomial approximation for all continuous functions on [-1, 1]. Secondly, on the ground of probability theory, we discuss the p-average errors of Hermite-Fejr interpolation sequence based on the extended Chebyshev nodes of the second kind on the Wiener space. By our results we know that for 1≤ p 【 ∞ and 2≤ q 【 ∞, the p-average errors of Hermite-Fejr interpolation approximation sequence based on the extended Chebyshev nodes of the second kind are weakly equivalent to the p-average errors of the corresponding best polynomial approximation sequence for L q -norm approximation. In comparison with these results, we discuss the p-average errors of Hermite-Fejr interpolation approximation sequence based on the Chebyshev nodes of the second kind and the p-average errors of the well-known Bernstein polynomial approximation sequence on the Wiener space.
