Sparse Stochastic Optimal Control under Control-Dependent Diffusion and Time-Varying Dynamics

Sparse Stochastic Optimal Control under Control-Dependent Diffusion and Time-Varying Dynamics | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Sparse Stochastic Optimal Control under Control-Dependent Diffusion and Time-Varying Dynamics YONG WANG, Lingyue Li, Haopeng Deng, Zhu Luo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6612631/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract We propose a unified framework for sparse stochastic optimal control in systems governed by time-varying dynamics and control-dependent diffusion—key features in robotic manipulators, energy systems, and other real-world applications. In contrast to conventional models assuming control-independent noise, our formulation explicitly captures the feedback between control effort and stochastic disturbances. This leads to a modified Hamilton–Jacobi–Bellman (HJB) equation that is nonconvex, nonsmooth, and nonmonotone. To address these challenges, we develop a relaxed viscosity solution framework that ensures analytical well-posedness. We also establish structural conditions under which sparse $L_0$-optimal control can be exactly recovered via its convex $L_1$ relaxation, leading to provable bang–off–bang strategies. Numerical simulations on robotic arms and photovoltaic–battery systems demonstrate the effectiveness of the proposed approach, showing superior control sparsity, robustness to noise, and safety guarantees under uncertainty. The results suggest our method offers a principled and scalable solution for real-time decision-making in noisy, resource-constrained environments. Applied Mathematics Sparse control stochastic optimal control control-dependent diffusion Hamilton–Jacobi–Bellman equation viscosity solutions Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6612631","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":453307929,"identity":"1c6d5126-2c93-4630-8182-74d30c35b902","order_by":0,"name":"YONG WANG","email":"","orcid":"https://orcid.org/0009-0007-7468-7860","institution":"School of Arts and Sciences, Guangzhou Maritime University, Guangzhou 510725, China","correspondingAuthor":false,"prefix":"","firstName":"YONG","middleName":"","lastName":"WANG","suffix":""},{"id":453307930,"identity":"8a905b14-d753-49ed-991e-b21bae7c80ad","order_by":1,"name":"Lingyue 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