{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T10:49:05Z","timestamp":1775731745258,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T00:00:00Z","timestamp":1775692800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper proposes an integrated robust\u2013learning control framework for uncertain systems with external disturbances. An H\u221e state-feedback controller is first synthesized to ensure closed-loop stability and a prescribed disturbance attenuation level under norm-bounded uncertainties. Building on this robust baseline, the Deep Deterministic Policy Gradient (DDPG) is used to refine the H\u221e feedback gains online to improve tracking and transient performance while reducing the conservatism of fixed robust gains. To improve the exploration process in reinforcement learning, a tracking-error-guided mechanism is developed. It adaptively adjusts the exploration intensity by means of tracking error energy, promoting reasonable exploration under steady-state conditions while suppressing excessive exploration during large transients, thereby improving both learning efficiency and system transient performance. The simulation results verify the effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/a19040291","type":"journal-article","created":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T09:46:23Z","timestamp":1775727983000},"page":"291","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Improved H\u221e Tracking Controller for Uncertain Systems Based on DDPG with Improved Exploration Strategy"],"prefix":"10.3390","volume":"19","author":[{"given":"Yujie","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Automation and Zhejiang Key Laboratory of Intelligent Perception and Control for Complex Systems, College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5737","DOI":"10.1109\/TAC.2022.3226703","article-title":"Adaptive finite-time tracking control of nonlinear systems with dynamics uncertainties","volume":"68","author":"Wang","year":"2022","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"5498","DOI":"10.1109\/TAC.2021.3050446","article-title":"Indirect adaptive MPC for discrete-time LTI systems with parametric uncertainties","volume":"66","author":"Dhar","year":"2021","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1109\/TASE.2024.3350020","article-title":"Disturbance-compensation-based predictive sliding mode control for aero-engine networked systems with multiple uncertainties","volume":"22","author":"Song","year":"2025","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"374","DOI":"10.3934\/mmc.2024030","article-title":"A frequency domain-based loop shaping procedure for the parameter estimation of the fractional-order tilt integral derivative controller","volume":"4","author":"Dakua","year":"2024","journal-title":"Math. Model. Control"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"102912","DOI":"10.1016\/j.mechatronics.2022.102912","article-title":"Combined design of robust controller and disturbance observer in a fixed-order H\u221e control framework","volume":"88","year":"2022","journal-title":"Mechatronics"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Qin, C., Qiao, X., Wang, J., and Zhang, D. (2022). Robust trajectory tracking control for continuous-time nonlinear systems with state constraints and uncertain disturbances. 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Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"8096","DOI":"10.1109\/TAC.2024.3410912","article-title":"Adaptive robust tracking control with active learning for linear systems with ellipsoidal bounded uncertainties","volume":"69","author":"Ma","year":"2024","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"8258","DOI":"10.1109\/TCYB.2021.3049555","article-title":"DDPG-Based adaptive robust tracking control for aerial manipulators with decoupling approach","volume":"52","author":"Liu","year":"2021","journal-title":"IEEE Trans. Cybern."},{"key":"ref_12","first-page":"5427","article-title":"Robust H\u221e output-feedback control for lane keeping of autonomous ground vehicles considering the system uncertainties","volume":"239","author":"Xu","year":"2025","journal-title":"Proc. Inst. Mech. Eng. Part D J. Automob. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1007\/s40435-024-01535-z","article-title":"Robust fault-tolerant control and application in DCS with uncertainty and time delay","volume":"13","author":"Ri","year":"2025","journal-title":"Int. J. Dyn. Control"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.isatra.2023.12.028","article-title":"Robust ultimately boundedness control of uncertain delayed systems under time-varying reference and external disturbance","volume":"146","author":"Ghaffari","year":"2024","journal-title":"ISA Trans."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4787","DOI":"10.1109\/TFUZZ.2024.3409175","article-title":"Adaptive robust fuzzy sliding mode control for wastewater treatment processes","volume":"32","author":"Han","year":"2024","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"121","DOI":"10.3934\/mmc.2025009","article-title":"Position tracking control of nonholonomic mobile robots via H\u221e-based adaptive fractional-order sliding mode controller","volume":"5","author":"Kumar","year":"2025","journal-title":"Math. Model. Control"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"9621","DOI":"10.1109\/TCYB.2021.3060736","article-title":"Reinforcement-learning-based disturbance rejection control for uncertain nonlinear systems","volume":"52","author":"Ran","year":"2021","journal-title":"IEEE Trans. Cybern."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4330","DOI":"10.1109\/TNNLS.2019.2954983","article-title":"Reinforcement learning-based optimal stabilization for unknown nonlinear systems subject to inputs with uncertain constraints","volume":"31","author":"Zhao","year":"2019","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"103028","DOI":"10.1016\/j.jprocont.2023.103028","article-title":"Robust safe reinforcement learning control of unknown continuous-time nonlinear systems with state constraints and disturbances","volume":"128","author":"Zhang","year":"2023","journal-title":"J. Process Control"},{"key":"ref_20","first-page":"7193","article-title":"Online robust reinforcement learning with model uncertainty","volume":"34","author":"Wang","year":"2021","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5492","DOI":"10.1109\/TNNLS.2021.3070852","article-title":"Adaptive observation-based efficient reinforcement learning for uncertain systems","volume":"33","author":"Ran","year":"2021","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1372","DOI":"10.1109\/TCYB.2015.2417170","article-title":"Reinforcement-learning-based robust controller design for continuous-time uncertain nonlinear systems subject to input constraints","volume":"45","author":"Liu","year":"2015","journal-title":"IEEE Trans. Cybern."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1335","DOI":"10.1109\/TSMC.2023.3325959","article-title":"Reinforcement learning-based adaptive finite-time performance constraint control for nonlinear systems","volume":"54","author":"Li","year":"2023","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/s10489-024-05932-x","article-title":"Neural network-based adaptive reinforcement learning for optimized backstepping tracking control of nonlinear systems with input delay","volume":"55","author":"Zhu","year":"2025","journal-title":"Appl. Intell."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"23987","DOI":"10.1007\/s00521-023-08993-0","article-title":"Reinforcement learning-based robust optimal tracking control for disturbed nonlinear systems","volume":"35","author":"Fan","year":"2023","journal-title":"Neural Comput. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1515\/acsc-2016-0030","article-title":"Analysis and comparison of the stability of discrete-time and continuous-time linear systems","volume":"26","author":"Kaczorek","year":"2016","journal-title":"Arch. Control Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1080\/00207728608926816","article-title":"Memoryless feedback control in uncertain dynamic delay systems","volume":"17","author":"Basher","year":"1986","journal-title":"Int. J. Syst. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/0005-1098(86)90045-2","article-title":"A Riccati equation approach to the stabilization of uncertain linear systems","volume":"22","author":"Petersen","year":"1986","journal-title":"Automatica"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"7025","DOI":"10.1016\/S0009-2509(01)00339-6","article-title":"Robust iterative learning control with applications to injection molding process","volume":"56","author":"Gao","year":"2001","journal-title":"Chem. Eng. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1321","DOI":"10.1016\/j.conengprac.2013.05.009","article-title":"H\u221e design of 2D controller for batch processes with uncertainties and interval time-varying delays","volume":"21","author":"Wang","year":"2013","journal-title":"Control Eng. Pract."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2084","DOI":"10.1109\/TII.2014.2350452","article-title":"Temperature control of industrial coke furnace using novel state space model predictive control","volume":"10","author":"Zhang","year":"2014","journal-title":"IEEE Trans. Ind. Inform."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/4\/291\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T09:50:28Z","timestamp":1775728228000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/4\/291"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,9]]},"references-count":31,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2026,4]]}},"alternative-id":["a19040291"],"URL":"https:\/\/doi.org\/10.3390\/a19040291","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,9]]}}}