{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:55:57Z","timestamp":1777715757558,"version":"3.51.4"},"reference-count":21,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[2000,5,1]],"date-time":"2000-05-01T00:00:00Z","timestamp":957139200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2000,5]]},"abstract":"<jats:p>A neural-network controller operating in discrete time is shown to result in stable trajectory tracking for rigid and elastic-joint robots. The technique assumes continuous-time state feedback. The proof of stability uses discrete-time Lyapunov functions. For the elastic-joint case, a discrete-time version of the adaptive backstepping technique is used. The result is that the neural network can be run at a very slow control rate, suitable for online calculations. The neural network used is referred to as the CMAC-RBF Associative Memory (CRAM), a modification of Albus\u2019s Cerebellar Model Arithmetic Computer (CMAC) algorithm using radial basis functions (RBFs). Simulation results are provided for a two-link planar elastic-joint robot and show that performance can be improved by using a larger network at a slower control rate.<\/jats:p>","DOI":"10.1177\/02783640022067003","type":"journal-article","created":{"date-parts":[[2004,12,17]],"date-time":"2004-12-17T20:23:10Z","timestamp":1103314990000},"page":"511-525","source":"Crossref","is-referenced-by-count":11,"title":["Discrete-Time Lyapunov Design for Neuroadaptive Control of Elastic-Joint Robots"],"prefix":"10.1177","volume":"19","author":[{"given":"C. J. B.","family":"Macnab","sequence":"first","affiliation":[{"name":"University of Toronto Institute for Aerospace Studies, 4925 Dufferin St.,                         Downsview, Ontario, Canada M3H 5T6"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G. M. T.","family":"D\u2019Eleuterio","sequence":"additional","affiliation":[{"name":"University of Toronto Institute for Aerospace Studies, 4925 Dufferin St.,                         Downsview, Ontario, Canada M3H 5T6"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2000,5,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1115\/1.3426922"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1115\/1.3426923"},{"key":"atypb3","unstructured":"Albus, J. 1981. Brains, Behaviour, and Robotics. 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