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Full-Text Articles in Physical Sciences and Mathematics
Almost Sure Asymptotic Stabilization Of Differential Equations With Time-Varying Delay By Lévy Noise, Dezhi Liu, Weiqun Wang, Jose Luis Menaldi
Almost Sure Asymptotic Stabilization Of Differential Equations With Time-Varying Delay By Lévy Noise, Dezhi Liu, Weiqun Wang, Jose Luis Menaldi
Mathematics Faculty Research Publications
This paper aims to determine that the Lévy noise can stabilize the given differential equations with time-varying delay, which has generalized the Brownian motion case. An analysis is developed and sufficient conditions on the stabilization for stochastic differential equations with time-varying delay are presented. Our stabilization criteria is in terms of linear matrix inequalities (LMIs), whence the feedback controls can be designed more easily in practice.
Stochastic Approximation Algorithms With Applications To Particle Swarm Optimization, Adaptive Optimization, And Consensus, Quan Yuan
Wayne State University Dissertations
In this dissertation, we present three problems arising in recent applications of stochastic approximation methods. In Chapter 2, we use stochastic approximation to analyze Particle Swarm Optimization (PSO) algorithm. We introduce four coefficients and rewrite the PSO procedure as a stochastic approximation type iterative algorithm. Then we analyze its convergence using weak convergence method. It is proved that a suitably scaled sequence of swarms converge to the solution of an ordinary differential equation. We also establish certain stability results. Moreover, convergence rates are ascertained by using weak convergence method. A centered and scaled sequence of the estimation errors is shown …