{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T18:08:32Z","timestamp":1788804512036,"version":"build-2803163510"},"reference-count":15,"publisher":"L and H Scientific Publishing, LLC","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["DNC"],"published-print":{"date-parts":[[2027,3,1]]},"abstract":"<jats:p>This study focuses on determining the minimum energy control for fractional delay systems. The optimal energy performance index for such systems is derived using solutions obtained through the Laplace transform. The proposed control strategy ensures the system transitions from its initial state to the desired final state with minimal energy consumption. The approach is further extended to accommodate various control types. To support the theoretical findings, the numerical examples along with graphical simulations are provided and discussed.<\/jats:p>","DOI":"10.5890\/dnc.2027.03.010","type":"journal-article","created":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T17:41:02Z","timestamp":1788802862000},"page":"135-146","source":"Crossref","is-referenced-by-count":0,"title":["Revolutionizing Control in Fractional Delay Systems with Minimum Energy"],"prefix":"10.5890","volume":"16","author":[{"given":"R. Joice","family":"Nirmala","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A. Mathan","family":"Kumar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"7015","published-online":{"date-parts":[[2026,9,7]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","unstructured":"[1] Klamka, J. (1976), Relative controllability and minimum energy control of linear systems with distributed delays in control, IEEE Transactions on Automatic Control, 4, 594-595.","DOI":"10.1109\/TAC.1976.1101280"},{"key":"ref2","doi-asserted-by":"crossref","unstructured":"[2] Agrawal, O.P. (2004), A general formulation and solution scheme for fractional optimal control problems, Nonlinear Dynamics, 38, 323-337.","DOI":"10.1007\/s11071-004-3764-6"},{"key":"ref3","unstructured":"[3] Bus\u0142owicz, M. and Kaczorek, T. (2007), Reachability and minimum energy control of positive linear discrete-time systems with multiple delays in state and control, Measurement Automation and Monitoring, 53, 40-45."},{"key":"ref4","unstructured":"[4] Mozyrska, D. and Torres, D.F.M. (2010), Minimal modified energy control for fractional linear control systems with the Caputo derivative, Carpathian Journal of Mathematics, 26, 210-221."},{"key":"ref5","unstructured":"[5] Klamka, J. 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(2013), Minimum energy control of fractional positive continuous-time linear systems with bounded inputs, International Journal of Applied Mathematics and Computer sciences, \\text{23}, 725-730.","DOI":"10.2478\/amcs-2013-0054"},{"key":"ref10","doi-asserted-by":"crossref","unstructured":"[10] Kaczorek, T. (2014), An extension of Klamka's method of minimum energy control to fractional positive discrete-time linear systems with bounded inputs, Bulletin of the Polish Academy of Science, 62, 227-231.","DOI":"10.2478\/bpasts-2014-0022"},{"key":"ref11","doi-asserted-by":"crossref","unstructured":"[11] Nirmala, R.J., Balachandran, K., Rodriguez-Germa, L., and Trujillo, J.J. (2016), Controllability of nonlinear fractional delay dynamical systems, Reports on Mathematical Physics, 77, 87-104","DOI":"10.1016\/S0034-4877(16)30007-6"},{"key":"ref12","doi-asserted-by":"crossref","unstructured":"[12] Nirmala, R.J. and Balachandran, K. (2017), Relative controllability of fractional delay integrodifferential systems with multiple delays in control, Kybernetika, 53, 161-178.","DOI":"10.14736\/kyb-2017-1-0161"},{"key":"ref13","doi-asserted-by":"crossref","unstructured":"[13] Sivasankar, S. and Udhayakumar, R. (2022), A note on approximate controllability of second-order neutral stochastic delay integro-differential evolution inclusions with impulses, Mathematical Methods in Applied Sciences, \\text{45}, 6650-6676.","DOI":"10.1002\/mma.8198"},{"key":"ref14","doi-asserted-by":"crossref","unstructured":"[14] Shukla, A., Sukavanam, N., and Pandey, D.N. (2014), Controllability of semilinear stochastic system with multiple delays in control, IFAC Proceeding Volumes, 47, 306-312.","DOI":"10.3182\/20140313-3-IN-3024.00107"},{"key":"ref15","doi-asserted-by":"crossref","unstructured":"[15] Shukla, A. and Sukavanam, N. (2021), Interior approximate controllability of second order semilinear control systems, International Journal of Control, 97, 615-624.","DOI":"10.1080\/00207179.2022.2161013"}],"container-title":["The interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T17:41:44Z","timestamp":1788802904000},"score":1,"resource":{"primary":{"URL":"https:\/\/lhscientificpublishing.com\/index.php\/DNC\/article\/view\/2480"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,7]]},"references-count":15,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2027,3,1]]}},"URL":"https:\/\/doi.org\/10.5890\/dnc.2027.03.010","relation":{},"ISSN":["2164-6376","2164-6414"],"issn-type":[{"value":"2164-6376","type":"print"},{"value":"2164-6414","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,7]]}}}