Bound Estimation of Some Special Functions

This article estimates bounds of several special functions. It also gives mathematical proofs and graphs of the corresponding functions. The results are applicable in aspect of inequalities.

Sliding repetitive control with adaptive bound estimation for motion systems liable to periodic exogenous signals

Periodic exogenous signals often exist in motion systems, especially those involving one or more rotating elements. These periodic exogenous signals deteriorate the performance of motion systems, and these adverse effects cannot be practically eliminated by straightforwardly increasing feedback control gains due to sensor noise, actuator saturation, and unmodeled plant dynamics. This paper describes a sliding repetitive controller for motion systems subject to periodic exogenous signals. Moreover, an adaptive law for bound estimation is devised to ensure the presence of a sliding motion for both repetitive learning and disturbance observation. The tracking motion system of a disk drive is considered in practice, and a traditional repetitive controller is also implemented for performance comparisons with the proposed scheme. Experimental results are reported in this paper, showing the efficacy of the proposed scheme.

Extract the information from big data with randomly distributed noise

In this manuscript, a purely data-driven statistical regularization method is proposed for extracting the information from big data with randomly distributed noise. Since the variance of the noise may be large, the method can be regarded as a general data preprocessing method in ill-posed problems, which is able to overcome the difficulty that the traditional regularization method is unable to solve, and has superior advantage in computing efficiency. The unique solvability of the method is proved, and a number of conditions are given to characterize the solution. The regularization parameter strategy is discussed, and the rigorous upper bound estimation of the confidence interval of the error in the L 2 L^{2} norm is established. Some numerical examples are provided to illustrate the appropriateness and effectiveness of the method.