Asymptotic optimality for consensus-type stochastic approximation algorithms using iterate averaging

This paper introduces a post-iteration averaging algorithm to achieve asymptotic optimality in convergence rates of stochastic approximation algorithms for consensus control with structural constraints. The algorithm involves two stages. The first stage is a coarse approximation obtained using a sequence of large stepsizes. Then, the second stage provides a refinement by averaging the iterates from the first stage. We show that the new algorithm is asymptotically efficient and gives the optimal convergence rates in the sense of the best scaling factor and ＇smallest＇ possible asymptotic variance.

EFFECTS OF MICROSTRUCTURE ON THE MACROSCOPIC ELASTO-PLASTIC PROPERTIES OF METAL MATRIX COMPOSITES

The generalized self-consistent finite-element iterative averaging method was adopted to analyze the elasto-plastic tensile properties of SiC whiskers reinforced aluminum matrix composites. The effects of varying fiber's aspect ratio and volume fraction on the macroscopic elasto-plastic deformation of the composites were studied. By the analysis of microscopic stress fields, the relation between the propagation of the elasto-plastic region in the matrix and the macroscopic elasto-plastic deformation of composites was discussed. It was found that the propagation of the plastic region in the matrix between the fiber's ends would affect prominently the elasto-plastic tensile behaviour of the composites. It was shown that the characterization of the stress-strain response in terms of the 0.2% offset yield strength is incomplete.

Boundedness of iterated spherical average

The iterated spherical average∆(A1)^(N)is an important operator in harmonic analysis,and has very important applications in approximation theory and probability theory,where∆is the Laplacian,A_(1)is the unit spherical average and(A1)^(N)is its iteration.In this paper,we mainly study the sufficient and necessary conditions for the boundedness of this operator in Besov-Lipschitz space,and prove the boundedness of the operator in Triebel-Lizorkin space.Moreover,we use above conclusions to improve the existing results of the boundedness of this operator in L^(p)space.

Lifted System Framework for Learning Control with Different Trial Lengths

This paper addresses an iterative learning control(ILC) design problem for discrete-time linear systems with randomly varying trial lengths. Due to the variation of the trial lengths, a stochastic matrix and an iteration-average operator are introduced to present a unified expression of ILC scheme. By using the framework of lifted system, the learning convergence condition of ILC in mathematical expectation is derived without using λ-norm. It is shown that the requirement on classic ILC that all trial lengths must be identical is mitigated and the identical initialization condition can be also removed. In the end, two illustrative examples are presented to demonstrate the performance and the effectiveness of the proposed ILC scheme for both time-invariant and time-varying linear systems.

UNIFORM QUADRATIC CONVERGENCE OF A MONOTONE WEIGHTED AVERAGE METHOD FOR SEMILINEAR SINGULARLY PERTURBED PARABOLIC PROBLEMS＊

This paper deals with a monotone weighted average iterative method for solving semilinear singularly perturbed parabolic problems. Monotone sequences, based on the ac- celerated monotone iterative method, are constructed for a nonlinear difference scheme which approximates the semilinear parabolic problem. This monotone convergence leads to the existence-uniqueness theorem. An analysis of uniform convergence of the monotone weighted average iterative method to the solutions of the nonlinear difference scheme and continuous problem is given. Numerical experiments are presented.