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This article focuses on a class of two-time-scale functional stochastic differential equations, where the phase space of the segment processes is infinite-dimensional. The systems under consideration have a fast-varying component and a slowly varying one. First, the ergodicity of the fast-varying component is obtained. Then inspired by the Khasminskii’s approach, an averaging principle, in the sense of convergence in thepth moment uniformly in time within a finite time interval, is developed. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on dynamic modelling and real-time control for a parallel manipulator with flexible link. The Lagrange principle and assumed modes method (AMM) substructure technique is presented to formulate the dynamic modelling of a two-degrees-of-freedom (DOF) parallel manipulator with flexible links. Then, the singular perturbation technique (SPT) is used to decompose the nonlinear dynamic system into slow time-scale and fast time-scale subsystems. Furthermore, the SPT is employed to transform the differential algebraic equations (DAEs) for kinematic constraints into explicit ordinary differential equations (ODEs), which makes real-time control possible. In addition, a novel composite control scheme is presented; the computed torque control is applied for a slow subsystem and the Ha technique for the fast subsystem, taking account of the model uncertainty and outside disturbance. The simulation results show the composite control can effectively achieve fast and accurate tracking control. [ABSTRACT FROM AUTHOR]