{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T05:29:51Z","timestamp":1761802191231,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T00:00:00Z","timestamp":1761523200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62103282","12071292","12131007","12071044"],"award-info":[{"award-number":["62103282","12071292","12131007","12071044"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper explores the optimal control issue for a linear\u2013quadratic\u2013Gaussian (LQG) system under the conditions of imperfect feedback and constraints related to energy harvesting. The system is equipped with various energy options, which allow it to gather energy for information transmission while also receiving imperfect feedback from an auxiliary filter that estimates packet loss. The primary goal of this study is to jointly design the energy selector and the controller to achieve an optimal balance between transmission costs and control performance. Initially, we separate the controller\u2019s synthesis task from the energy selection task. The subproblem of optimal controller synthesis is characterized by a Riccati equation that takes continuous packet loss into account. Simultaneously, the energy selection task, influenced by imperfect feedback and constraints on energy costs, is reformulated as a Markov decision process (MDP) that operates with perfect acknowledgments through iterative updates of state information. Ultimately, the optimal energy selection policy that guarantees filtering performance is derived by solving a Bellman equation. The effectiveness of the proposed approach is confirmed through simulation results.<\/jats:p>","DOI":"10.3390\/axioms14110791","type":"journal-article","created":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T03:44:39Z","timestamp":1761795879000},"page":"791","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Energy Management and Control for Linear\u2013Quadratic\u2013Gaussian Systems with Imperfect Acknowledgments and Energy Constraints"],"prefix":"10.3390","volume":"14","author":[{"given":"Zhiping","family":"Ju","sequence":"first","affiliation":[{"name":"School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China"}]},{"given":"Lijun","family":"Guo","sequence":"additional","affiliation":[{"name":"College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China"}]},{"given":"Jiajia","family":"Li","sequence":"additional","affiliation":[{"name":"College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China"}]},{"given":"Qiangchang","family":"Ju","sequence":"additional","affiliation":[{"name":"Institute of Applied Physics and Computational Mathematics, Beijing 100088, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2058","DOI":"10.1109\/TWC.2014.2379642","article-title":"Energy-efficient spectrum sensing for cognitive radio enabled remote state estimation over wireless channels","volume":"14","author":"Cao","year":"2014","journal-title":"IEEE Trans. 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