[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-126642-en":3,"doc-seo-126642-105":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":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},126642,549768064778,"Finn","https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8",8,"Research & Report","Model-free tracking control of complex dynamical trajectories with machine learning","Nonlinear tracking control that enables a system to follow a desired trajectory is central to robotics and many civil and defense applications. The work develops a model-free machine-learning framework for a two-arm robotic manipulator using only partially observed states, with control realized via reservoir computing. Stochastic inputs train the model by mapping the observed partial state to its immediate future. During deployment, the learned future component is replaced by the desired observational vector from the reference trajectory, and results show robustness to measurement noise, disturbances, and uncertainties across periodic and chaotic signals.","arXiv :2309 . 11470v1 [ cs .RO] 20 Sep 2023  \nModel-free tracking control of complex dynamical trajectories with machine learning  \nZheng-Meng Zhai, 1 Mohammadamin Moradi, 1 Ling-Wei Kong, 1  \nBryan Glaz,2 Mulugeta Haile,3 and Ying-Cheng Lai 1, 4, ∗  \n1 School of Electrical, Computer and Energy Engineering,  \nArizona State University, Tempe, AZ 85287, USA  \n2 Vehicle Technology Directorate, CCDC Army Research Laboratory,  \n2800 Powder Mill Road, Adelphi, MD 20783-1138, USA  \n3 Vehicle Technology Directorate, CCDC Army Research Laboratory,  \n6340 Rodman Road, Aberdeen Proving Ground, MD 21005-5069, USA  \n4 Department of Physics, Arizona State University, Tempe, Arizona 85287, USA  \n(Dated: September 21, 2023)  \nNonlinear tracking control enabling a dynamical system to track a desired trajectory is fundamental to robotics, serving a wide range of civil and defense applications. In control engineering, designing tracking control requires complete knowledge of the system model and equations. We develop a model-free, machine-learning framework to control a two-arm robotic manipulator using only partially observed states, where the controller is realized by reservoir computing. Stochastic input is exploited for training, which consists of the observed partial state vector as the first and its immediate future as the second component so that the neural machine regards the latter as the future state of the former. In the testing (deployment) phase, the immediate-future component is replaced by the desired observational vector from the reference trajectory. We demonstrate the effectiveness of the control framework using a variety of periodic and chaotic signals, and establish its robustness against measurement noise, disturbances, and uncertainties.  \nINTRODUCTION  \nThe traditional field of controlling chaotic dynamical systems mostly deals with the problem of utilizing small perturbations to transform a chaotic trajectory into a desired periodic one [1] . The basic principle is that the dynamically invariant set that generates chaotic motions contains an infinite number of unstable periodic orbits. For any desired system performance, it is often possible to find an unstable periodic orbit whose motion would produce the required behavior. The problem then becomes one to stabilize the system’s state-space or phasespace trajectory around the desired unstable periodic orbit, which can be achieved through linear control in the vicinity of the orbit, thereby requiring only small control perturbations. The control actions can be calculated from the locations and the eigenvalues of the target orbit, which are often experimentally accessible through a measured time series, without the need to know the actual system equations [1–4] . Controlling chaos can thus be done in a model-free, entirely data-driven manner, and the control is most effective when the chaotic behavior is generated by a low-dimensional invariant set, e.g., one with one unstable dimension or one positive Lyapunov exponent. However, for high-dimensional dynamical systems, controlling complex nonlinear dynamical networks is an active area of research [5–7] .  \nThe goal of tracking control is to design a control law to enable the output of a dynamical system (or a process) to track a given reference signal. For linear feedback systems, tracking control can be mathematically designed  \n∗ [Ying-Cheng.Lai@asu.edu](Ying-Cheng.Lai@asu.edu)  \nwith rigorous guarantee of stability [8] . However, nonlinear tracking control is more challenging, especially when the goal is to make a system to track a complex signal. In robotics, for instance, a problem is to design control actions to make the tip of a robotic arm, or the end effector, to follow a complicated or chaotic trajectory. In control engineering, designing tracking control typically requires complete knowledge of the system model and equations. Existing methods for this include feedback linearization [9], back-stepping control [10]","cbCairiCVjANvQmF","https://ap.wps.com/l/cbCairiCVjANvQmF","pdf",4007632,1,16,"English","en",105,"# Introduction\n## Background on controlling chaotic dynamical systems\n## Tracking control objectives and challenges\n## Motivation for model-free data-driven and machine-learning control","[{\"question\":\"What problem does the paper address in tracking control?\",\"answer\":\"It addresses how to design a tracking controller for complex, including chaotic, trajectories when a complete and accurate system model is unavailable.\"},{\"question\":\"How does the proposed framework handle partial observations?\",\"answer\":\"It uses only partially observed state information, training a reservoir-computing controller with observed state vectors and their immediate future.\"},{\"question\":\"What does the framework replace during deployment/testing?\",\"answer\":\"During deployment, the immediate-future component used during training is replaced by the desired observational vector taken from the reference trajectory.\"}]","Model-free tracking control of complex dynamical trajectories with machine learning | 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problem does the paper address in tracking control?","Question",{"text":75,"@type":76},"It addresses how to design a tracking controller for complex, including chaotic, trajectories when a complete and accurate system model is unavailable.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed framework handle partial observations?",{"text":80,"@type":76},"It uses only partially observed state information, training a reservoir-computing controller with observed state vectors and their immediate future.",{"name":82,"@type":73,"acceptedAnswer":83},"What does the framework replace during deployment/testing?",{"text":84,"@type":76},"During deployment, the immediate-future component used during training is replaced by the desired observational vector taken from the reference 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