The DOI matches its Crossref record; 45 of the 45 references it cites were found in a registry or an index.
ADP-Based Decentralized Controller Design for Nonlinear Time-Delay Interconnected Systems
Abstract
The control of industrial processes which can be generally described by nonlinear time-delay interconnected systems is very important. A decentralized control method based on adaptive dynamic programming (ADP) is proposed in this article, which can solve the control and stability problem for nonlinear time-delay interconnected systems using past state data and interconnection information. First, the form of nonlinear interconnected systems with state delay is given. Based on such systems, the subsystems are reconstructed by adding the upper bound of the interconnection part to the cost function. New cost functions are constructed which include a series of Hamilton–Jacobi–Bellman (HJB) equations with Lyapunov–Krasovskii (L–K) function, where the past state data and interconnection information are employed. Then, the control problem can be dealt with by solving the HJB equations. The HJB equations can be solved by the critic learning method based on ADP, where the critic neural networks (NNs) are applied to estimate the optimal cost function. The weights can be calculated by the gradient descent method, and the control law can be obtained. Subsequently, the stability of the closed-loop system is proved in the sense of uniformly ultimately bounded (UUB). Finally, simulation results verify the effectiveness of the proposed method by a nonlinear time-delay interconnected system and two-stage chemical reactors.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Citations
Cites
Reinforcement Learning: An Introduction
Johnson, J. D., Li, J., & Chen, Z. (2000) · Neurocomputing · doi:10.1016/s0925-2312(00)00324-6 · Cited by 8,825
Wiley Series in Probability and Statistics
(2008) · Wiley series in probability and statistics · doi:10.1002/series1345 · Cited by 4,443
Lewis, F. L., Vrabie, D. L., & Syrmos, V. L. (2012) · doi:10.1002/9781118122631 · Cited by 2,020
Delay-dependent robust stabilization of uncertain state-delayed systems
Moon, Y. S., Park, P., Кwon, W. H., & Lee, Y. S. (2001) · International Journal of Control · doi:10.1080/00207170110067116 · Cited by 1,464
Further Improvement of Free-Weighting Matrices Technique for Systems With Time-Varying Delay
He, Y. M., Wang, Q., Xie, L., & Lin, C. (2007) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2006.887907 · Cited by 754
Adaptive control of nonlinearly parameterized systems: the smooth feedback case
Lin, W. T., & Qian, C. (2002) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2002.800773 · Cited by 634
Decentralized control: An overview
Bakule, L. (2008) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2008.03.004 · Cited by 585
Liu, D., Wang, D., & Li, H. (2013) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2013.2280013 · Cited by 352
Park, H. B., Jeung, E. T., Kim, J., & Lee, K. R. (2000) · IEEE Transactions on Fuzzy Systems · doi:10.1109/91.890325 · Cited by 256
Gu, Z., Shi, P. J., Yue, D., & Ding, Z. (2018) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2018.2802044 · Cited by 189
Cited by
Sorted by citations
Zhao, J., Karimi, H. R., Niu, B., & Zhao, X. (2025) · Neurocomputing · doi:10.1016/j.neucom.2025.131203 · Cited by 40
Liu, C., Chu, Z., Duan, Z., Zhang, H., & Ma, Z. (2024) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2024.3462718 · Cited by 28
Rahimi, F. (2024) · International Journal of Systems Science · doi:10.1080/00207721.2024.2440785 · Cited by 18
Adaptive dynamic programming-based fault tolerant control for nonlinear time-delay systems
Rahimi, F. (2024) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2024.115544 · Cited by 17
Liu, Z., Jiang, Z.-W., Sun, W., & Su, S. (2025) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2025.3573069 · Cited by 5
Metadata
- Authors
- Chen, N., Luo, Z., Li, B., Luo, B., Chen, J., Yang, C., & Gui, W.
- Affiliations
- Central South University (CN)
- Changsha University of Science and Technology (CN)
- Venue
- IEEE Transactions on Systems, Man, and Cybernetics: Systems
- Published
- 2024-08
- Volume
- 54
- Issue
- 8
- Pages
- 5035-5047
- ISSN
- 2168-2216 (ISSN-L)
- 2168-2232
- OpenAlex
- W4396680566
- Cited by
- 22
- References
- 45
- Citations by year
- 2026: 5 · 2025: 12 · 2024: 5
- FWCI
- 2.76
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- IEEE Transactions on Systems Man and Cybernetics Systems (publishedVersion)
- Funders
- Key Program of National Natural Science Foundation of China (62033014)
- Application Projects of Integrated Standardization and New Paradigm for Intelligent Manufacturing from the Ministry of Industry and Information Technology of China in 2016
- Fundamental Research Funds for the Central Universities of Central South University (2024ZZTS0781)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Adaptive Dynamic Programming Control
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Optimization
- Keywords
- adaptive dynamic programming, decentralized control, nonlinear time-delay systems, interconnected systems, state delay, Hamilton-Jacobi-Bellman equation, Lyapunov-Krasovskii functional, critic neural network, uniform ultimate boundedness, industrial process control
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
