[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84128-en":3,"doc-seo-84128-105":29,"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":11,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},84128,687197207057,"Sage","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Neural-ESO A Dual Pathway Architecture for Provably Robust Learning Based Control","A learning-enabled disturbance-rejection framework based on a Neural Extended State Observer (Neural-ESO) is presented to improve learning-based control reliability. Neural-ESO uses a dual-pathway design: a predictive neural pathway generates feedforward disturbance estimates to accelerate convergence, while a corrective conventional ESO compensates prediction errors and reduces over-reliance on the neural component. Lyapunov and small-gain analysis shows that enforcing a Lipschitz bound on the learning component guarantees uniform ultimate boundedness of closed-loop errors. Quadrotor landing experiments under strong, out-of-distribution ground effects demonstrate improved accuracy-robustness trade-offs and operational dependability across training, deployment, and transfer.","Neural-ESO: A Dual-Pathway Architecture for Provably Robust Learning-Based Control  \nFan Zhang 1 ,2 , Richie Suganda 1 ,2 , Jinfeng Chen 1 , Wenhua Liu 1 ,2 , Hantao Fu3 , Bin Hu 1 ,2 , Qin Lin 1 ,2  \narXiv :2607 .06535v 1 [ cs .RO] 7 Jul 2026  \nAbstract—A learning-enabled disturbance-rejection framework based on a Neural Extended State Observer (Neural-ESO) is presented in this letter. Unlike existing learning-based control methods that largely rely on the learned model once deployed, Neural-ESO adopts a dual-pathway architecture: a predictive pathway uses a neural network to provide a feedforward disturbance estimate that accelerates convergence, while a corrective pathway employs a conventional ESO to compensate prediction errors and prevent over-reliance on the neural component. Using Lyapunov theory and a small-gain analysis, we show that enforcing a Lipschitz bound on the learning component guarantees uniform ultimate boundedness of the closed-loop error dynamics. The proposed framework is validated on a quadrotor landing task subject to strong ground-effect disturbances across normal and out-of-distribution scenarios, demonstrating accuracyrobustness trade-off and greater operational reliability during training, deployment, and transfer compared with state-of-theart baselines. Video:[https://youtu.be/KVUX0SVO-dA. Code](https://youtu.be/KVUX0SVO-dA. Code) and example dataset: [https://github.com/fzhang327/Neural-ESO](https://github.com/fzhang327/Neural-ESO).  \nIndex Terms—Machine Learning for Robot Control, Robust/Adaptive Control, Aerial Systems: Mechanics and Control  \nI. INTRODUCTION  \nTIME-VARYING unknown disturbances are a fundamen  \ntal challenge for high-performance control of situated robots deployed in the real world. Take an unmanned aerial vehicle (UAV) as an example: such disturbances can arise from model uncertainty (e.g., parameter identification errors) and external effects (e.g., wind and payload variations) . To address these issues, a key question is how to measure the discrepancy between the known (nominal) model and the true system dynamics.  \nLearning-based control leverages deep neural networks (DNNs) to approximate either the full dynamics or modeling discrepancies [1]–[3] . A common strategy, referred to here as direct residual learning, learns the discrepancy by fitting the mismatch between model-predicted and measured states.  \nManuscript received: January, 29, 2026; Revised May, 7, Year; Accepted June, 11, 2026 .  \nThis paper was recommended for publication by Editor Jens Kober upon evaluation of the Associate Editor and Reviewers’ comments. This material is based upon work supported by the National Science Foundation under Grant No. 2525200. (Corresponding author: Qin Lin.)  \n1Fan Zhang, Richie Suganda, Jinfeng Chen, Wenhua Liu, Bin Hu, and Qin Lin are with the Department of Engineering Technology, University of Houston, [USA.](USA. qlin21@central.uh.edu)[ qlin21@central.uh.edu](USA. qlin21@central.uh.edu)  \n2Fan Zhang, Richie Suganda, Wenhua Liu, Bin Hu, and Qin Lin are with the Department of Electrical and Computer Engineering, University of Houston, USA  \n3Hantao Fu is with the Department of Electrical Engineering, Rice University, USA.  \nDigital Object Identifier (DOI): see top of this page.  \nFig. 1. Experimental validation under three scenarios. (a) Top left: Normal landing, where training and testing are performed in the same setting. (b) Top right: OOD with a slope placed near the landing zone. (c) Bottom: OOD highspeed near-ground lemniscate maneuvers under nonstationary turbulence.  \nFor autonomous drone landing, where ground effect acts asan unknown disturbance that can prevent landing, NeuralLander [1] learns and compensates this disturbance using deep learning. Despite their flexibility and minimal assumptionson disturbance structure, such approaches suffer from several limitations: (i) providing formal guarantees for learningenabled components remains a significant challenge,(ii)","cbCail3UKWgEESIo","https://ap.wps.com/l/cbCail3UKWgEESIo","pdf",2099671,5,1,"English","en",105,"# Introduction\n## Learning-based disturbance rejection\n## Limits of direct residual learning\n## Observer-based control and ESO\n## Research questions and dual-pathway design","[{\"question\":\"What problem does Neural-ESO address in learning-based control?\",\"answer\":\"Neural-ESO targets time-varying unknown disturbances that can cause poor performance or instability, especially when test conditions differ from training (out-of-distribution).\"},{\"question\":\"How does the dual-pathway architecture work?\",\"answer\":\"It uses a predictive pathway where a neural network provides a feedforward disturbance estimate to speed convergence, and a corrective pathway where a conventional ESO compensates prediction errors to avoid over-reliance on the neural part.\"},{\"question\":\"What stability guarantee does the method provide?\",\"answer\":\"Using Lyapunov theory and a small-gain analysis, the framework guarantees uniform ultimate boundedness by enforcing a Lipschitz bound on the learning component, while the dual-pathway ESO mitigates residual prediction 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problem does Neural-ESO address in learning-based control?","Question",{"text":75,"@type":76},"Neural-ESO targets time-varying unknown disturbances that can cause poor performance or instability, especially when test conditions differ from training (out-of-distribution).","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the dual-pathway architecture work?",{"text":80,"@type":76},"It uses a predictive pathway where a neural network provides a feedforward disturbance estimate to speed convergence, and a corrective pathway where a conventional ESO compensates prediction errors to avoid over-reliance on the neural part.",{"name":82,"@type":73,"acceptedAnswer":83},"What stability guarantee does the method provide?",{"text":84,"@type":76},"Using Lyapunov theory and a small-gain analysis, the framework guarantees uniform ultimate boundedness by enforcing a Lipschitz bound on the learning component, while the dual-pathway ESO mitigates residual prediction 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