{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T17:17:34Z","timestamp":1787505454581,"version":"build-2736575974"},"reference-count":40,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multiscale Model. Simul."],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:p>This work develops asynchronous stochastic approximation (SA) algorithms for networked systems with multiagents and regime-switching topologies to achieve consensus control. There are several distinct features of the algorithms: (1) In contrast to most of the existing consensus algorithms, the participating agents compute and communicate in an asynchronous fashion without using a global clock. (2) The agents compute and communicate at random times. (3) The regime-switching process is modeled as a discrete-time Markov chain with a finite state space. (4) The functions involved are allowed to vary with respect to time; hence, nonstationarity can be handled. (5) Multiscale formulation enriches the applicability of the algorithms. In the setup, the switching process contains a rate parameter $\\varepsilon&gt;0$ in the transition probability matrix that characterizes how frequently the topology switches. The algorithm uses a step-size $\\mu$ that defines how fast the network states are updated. Depending on their relative values, three distinct scenarios emerge. Under suitable conditions, it is shown that a continuous-time interpolation of the iterates converges weakly either to a system of randomly switching ordinary differential equations modulated by a continuous-time Markov chain or to a system of differential equations (an average with respect to certain measure). In addition, a scaled sequence of tracking errors converges to either a switching diffusion or a diffusion. Simulation results are presented to demonstrate these findings.<\/jats:p>","DOI":"10.1137\/120871614","type":"journal-article","created":{"date-parts":[[2013,8,15]],"date-time":"2013-08-15T10:48:00Z","timestamp":1376563680000},"page":"813-839","source":"Crossref","is-referenced-by-count":7,"title":["Asynchronous Stochastic Approximation Algorithms for Networked Systems: Regime-Switching Topologies and Multiscale Structure"],"prefix":"10.1137","volume":"11","author":[{"given":"G.","family":"Yin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Quan","family":"Yuan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Le Yi","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2013,8,15]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1109\/MCOM.2002.1024422"},{"key":"atypb2","unstructured":"P. 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Varga,\n                      Matrix Iterative Analysis\n                      , Spring-Verlag, Berlin, 2000.","DOI":"10.1007\/978-3-642-05156-2"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.75.1226"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpdc.2006.08.010"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-007-0145-1"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623403423709"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2005.847060"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2011.02.028"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1137\/110824450"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1109\/TPDS.2003.1167370"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139999354297"},{"key":"atypb37","unstructured":"G. Yin and Q. Zhang,\n                      Discrete-Time Markov Chains: Two-Time-Scale Methods and Applications\n                      , Springer, New York, 2005."},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1239\/aap\/1051201656"},{"key":"atypb39","doi-asserted-by":"crossref","unstructured":"G. Yin and C. 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