[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83716-en":3,"doc-seo-83716-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83716,4398048949847,"Eliana","https://ap-avatar.wpscdn.com/avatar/400002536579ef2da7f?_k=1778318612642679267",8,"Research & Report","Direct Data Driven Natural Gradient Descent for Control","Direct Data Driven Natural Gradient Descent for Control presents a direct data-driven control framework that uses Natural Gradient Descent (NGD) to synthesize interpretable and robust closed-loop policies without explicit model identification. Two data-driven NGD formulations incorporate closed-loop covariance via the Fisher Information Matrix (FIM) so gradient updates are preconditioned by intrinsic uncertainty. Stability and convergence are proved using semidefinite programs (SDPs), and the method is validated in simulations and on a ROSbot XL platform, outperforming LQR and standard baselines in convergence speed, robustness, and interpretability.","Direct Data Driven Natural Gradient Descent for  \nControl  \nRamin Esmzad, Farnaz Adib Yaghmaie, Bahare Kiumarsi, and Hamidreza Modares, Member, IEEE  \narXiv :2607 .03393v1 [ ee ss . SY] 3 Jul 2026  \nAbstract—This paper introduces a novel direct data-driven control framework based on Natural Gradient Descent (NGD) to design interpretable and robust closed-loop policies without requiring explicit model identification. We propose two datadriven NGD formulations that incorporate the closed-loop covariance matrix through the Fisher Information Matrix (FIM), allowing gradient updates to be preconditioned according to the system’s intrinsic uncertainty. Leveraging two distinct data-based parameterizations of the closed-loop system, our method enables stability-guaranteed policy synthesis directly from data. We provide theoretical guarantees for contraction and convergence using semidefinite programs (SDPs) and validate our framework in both simulations and on hardware on a ROSbot XL platform. The results demonstrate intuitive features compared to linearquadratic regulator (LQR) and standard data-driven baselines, particularly in terms of convergence speed, robustness, and control interpretability. This work bridges the gap between trajectory-oriented natural gradient methods and practical datadriven control design.  \nIndex Terms—Data-Driven Control, Linear Matrix Inequalities, Natural Gradient Descent, Robotics.  \nI. INTRODUCTION  \nThe integration of machine learning into control theory is revolutionizing how dynamical systems are controlled to achieve desired specifications. Machine learning offers the ability to learn from data, enabling control systems to adapt to changing conditions and optimize performance. Gradient descent (GD) is a fundamental algorithm for optimizing cost functions from data. In learning-based control, GD tunes the parameters of a system model or control policy to minimize modeling errors or implementation costs [1], [2], [3] . However, traditional GD-based control designs predominantly rely on indirect trajectory shaping via optimizing predefined cost functions. However, these methods require tedious, iterative tuning of cost parameters (e.g., weighting matrices in the linear-quadratic regulator (LQR)) and risk reward hacking, where resulting trajectories misalign with intended behavior [4] . This drives the need for frameworks that directly shape closed-loop trajectories with minimal heuristic adjustments. Alternatively, control tools can analyze GD optimization algorithms by treating them as dynamical systems to enable robust closed-loop optimization [5], [6], [7], [8] . This paper does not focus on this direction of using control to improve  \nRamin Esmzad and Hamidreza Modares are with the Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824 USA ([e-mail: modaresh@msu.edu](e-mail: modaresh@msu.edu)) .  \nFarnaz Adib Yaghmaie is with the Department of Electrical Engineering, Linkping University, 58183 Linkping, Sweden.  \nBahare Kiumarsi is with the Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824 USA.  \noptimization algorithms. To address these challenges,[9], [10] embeds gradient descent dynamics directly into the closed loop by using GD to parameterize the system dynamics. This forces system states to naturally evolve along a Lyapunovbased GD algorithm, providing geometric clarity, enhanced interpretability, and explicit robustness through systematic trajectory shaping.  \nHowever, the framework in [9], [10] requires known system dynamics, leaving it unsuited for data-driven scenarios with unknown parameters. While direct data-driven control strategies bypass model identification to design robust controllers directly from data [11], [12], [13], they have yet to leverage the geometric advantages of Natural Gradient Descent (NGD)  \n[14] . NGD accelerates convergence by accounting for the intrinsic geometry of the parameter","cbCainjZX9ZrvjcK","https://ap.wps.com/l/cbCainjZX9ZrvjcK","pdf",7098168,2,1,14,"English","en",105,"# Introduction\n## Direct data-driven NGD control formulation\n## Uncertainty-informed feedback via FIM\n## Theoretical guarantees and validation","[{\"question\":\"What problem does the paper address in control design?\",\"answer\":\"It targets data-driven closed-loop policy synthesis without requiring explicit model identification, while keeping the resulting policy interpretable and robust.\"},{\"question\":\"How does the framework use Natural Gradient Descent in the controller design?\",\"answer\":\"It embeds NGD geometry into the closed-loop dynamics using Fisher Information Matrix (FIM)-based preconditioning, so state evolution follows a natural-gradient flow.\"},{\"question\":\"What guarantees and evidence does the paper provide for performance?\",\"answer\":\"The paper establishes stability and convergence conditions using semidefinite programs (SDPs) and validates the approach in simulations and on a ROSbot XL robot, demonstrating improved convergence speed, robustness, and interpretability compared with LQR and data-driven 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problem does the paper address in control design?","Question",{"text":75,"@type":76},"It targets data-driven closed-loop policy synthesis without requiring explicit model identification, while keeping the resulting policy interpretable and robust.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the framework use Natural Gradient Descent in the controller design?",{"text":80,"@type":76},"It embeds NGD geometry into the closed-loop dynamics using Fisher Information Matrix (FIM)-based preconditioning, so state evolution follows a natural-gradient flow.",{"name":82,"@type":73,"acceptedAnswer":83},"What guarantees and evidence does the paper provide for performance?",{"text":84,"@type":76},"The paper establishes stability and convergence conditions using semidefinite programs (SDPs) and validates the approach in simulations and on a ROSbot XL robot, demonstrating improved convergence speed, robustness, and interpretability compared with LQR and data-driven 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