Linear manifold clustering for high dimensional data based on line manifold searching and fusing

High dimensional data clustering,with the inherent sparsity of data and the existence of noise,is a serious challenge for clustering algorithms.A new linear manifold clustering method was proposed to address this problem.The basic idea was to search the line manifold clusters hidden in datasets,and then fuse some of the line manifold clusters to construct higher dimensional manifold clusters.The orthogonal distance and the tangent distance were considered together as the linear manifold distance metrics. Spatial neighbor information was fully utilized to construct the original line manifold and optimize line manifolds during the line manifold cluster searching procedure.The results obtained from experiments over real and synthetic data sets demonstrate the superiority of the proposed method over some competing clustering methods in terms of accuracy and computation time.The proposed method is able to obtain high clustering accuracy for various data sets with different sizes,manifold dimensions and noise ratios,which confirms the anti-noise capability and high clustering accuracy of the proposed method for high dimensional data.

Gain Scheduling Control of Nonlinear Shock Motion Based on Equilibrium Manifold Linearization Model

The equilibrium manifold linearization model of nonlinear shock motion is of higher accuracy and lower complexity over other models such as the small perturbation model and the piecewise-linear model. This paper analyzes the physical significance of the equilibrium manifold linearization model, and the self-feedback mechanism of shock motion is revealed. This helps to describe the stability and dynamics of shock motion. Based on the model, the paper puts forwards a gain scheduling control method for nonlinear shock motion. Simulation has shown the validity of the control scheme.

Discrete-time based sliding-mode control of robot manipulators

Purpose-The purpose of this paper is to develop sliding mode control with linear and nonlinear manifolds in discrete-time domain for robot manipulators.Design/methodology/approach–First,a discrete linear sliding mode controller is designed to an n-link robot based on Gao’s reaching law.In the second step,a discrete terminal sliding mode controller is developed to design a finite time and high precision controller.The stability analysis of both controllers is presented in the presence of model uncertainties and external disturbances.Finally,sampling time effects on the continuous-time system outputs and sliding surfaces are discussed.Findings–Computer simulations on a three-link SCARA robot show that the proposed controllers are robust against model uncertainties and external disturbance.It was also shown that the sampling time has important effects on the closed loop system stability and convergence.Practical implications-The proposed controllers are low cost and easily implemented in practice in comparison with continuous-time ones.Originality/value-The novelty associated with this paper is the development of an approach to finite time and robust control of n-link robot manipulators in discrete-time domain.Also,obtaining an upper bound for the sampling time is another contribution of this work.