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Syst."],"published-print":{"date-parts":[[2026,9,30]]},"abstract":"<jats:p>Cyber-physical systems (CPS) have been increasingly deployed in many safety-critical industrial environments, where effective and efficient optimal control synthesis is vital for ensuring reliable system operation. The optimal control problem\u2014aimed at synthesizing an optimal control solution for a given control task\u2014remains a key challenge in CPS, particularly due to the intricate coupling of CPS\u2019s continuous and discrete (hybrid) dynamics. This challenge is further compounded in multi-component industrial systems, where the space of control solutions, including both discrete paths (control mode sequences) and continuous control parameters, is prone to the well-known state explosion problem. In this article, we propose an efficient path-encoding-based joint optimization method for the optimal control problem in multi-component hybrid systems. Our method jointly encodes paths and control parameters in a structured, integrated space, transforming the control synthesis problem into a well-defined optimization problem that can be efficiently solved by existing derivative-free optimization solvers. To further enhance efficiency, we introduce an optimized local path-encoding strategy, which decomposes the original one-dimensional path space into a multi-dimensional component-wise path space, enabling more effective exploration of paths. This strategy also reduces memory overhead and improves scalability. We implemented our method in a tool called PED, and experimental results show that it efficiently solves the optimal control problem in various complex multi-component hybrid systems. Moreover, the incorporation of our local path-encoding strategy further improves its performance.<\/jats:p>","DOI":"10.1145\/3769083","type":"journal-article","created":{"date-parts":[[2025,9,22]],"date-time":"2025-09-22T11:33:20Z","timestamp":1758540800000},"page":"1-28","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimal Control for Industrial Multi-Component CPS via Path-Encoding-Based Joint Optimization"],"prefix":"10.1145","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6170-5675","authenticated-orcid":false,"given":"Jiawan","family":"Wang","sequence":"first","affiliation":[{"name":"State Key Laboratory for Novel Software Technology, Nanjing University","place":["Nanjing, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-2550-0665","authenticated-orcid":false,"given":"Wenxia","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Novel Software Technology, Nanjing University","place":["Nanjing, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0517-7801","authenticated-orcid":false,"given":"Lei","family":"Bu","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Novel Software Technology, Nanjing University","place":["Nanjing, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3090-9568","authenticated-orcid":false,"given":"Xuandong","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Novel Software Technology, Nanjing University","place":["Nanjing, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2026,8,24]]},"reference":[{"key":"e_1_3_2_2_2","unstructured":"2024. 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