Observer-Based Adaptive Fuzzy Decentralized Optimal Control Design for Strict-Feedback Nonlinear Large-Scale Systems
Abstract
In this paper, the problem of adaptive fuzzy decentralized optimal control is investigated for a class of nonlinear large-scale systems in strict-feedback form. The considered nonlinear large-scale systems contain the unknown nonlinear functions and unmeasured states. By utilizing the fuzzy logic systems to approximate the unknown nonlinear functions and cost functions, a fuzzy state observer is established to estimate the unmeasured states. The control design is divided into two phases. First, by using the state observer and the backstepping design technique, a feedforward decentralized controller with parameters adaptive laws is designed, by which the original controlled strict-feedback nonlinear large-scale system is transformed into an equivalent affine nonlinear large-scale system. Second, by using adaptive dynamic programming theory, a feedback decentralized optimal controller is developed for the equivalent affine nonlinear system. The whole adaptive fuzzy decentralized optimal control scheme consists of a feedforward decentralized controller and a feedback decentralized optimal controller. It is shown that the proposed adaptive fuzzy decentralized optimal control approach can guarantee that all the signals in the closed-loop system are bounded, and the tracking errors converge to a small neighborhood of zero. In addition, the proposed control approach can guarantee that the cost functions are minimized. Simulation results are given to demonstrate the effectiveness of the proposed control approach.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The proposed method avoids requiring precise nonlinearity knowledge by approximating functions via RBFNNs using only sampled outputs, thereby reducing computational complexity.
“Unlike existing approaches [14], [25], the method avoids requiring precise nonlinearity knowledge by approximating functions via RBFNNs using only sampled outputs, thereby reducing computational complexity.”
From Neural Network-Aided Sampled-Data Control for a Class of Nonlinear Systems With Unknown Dynamics (2025) · cites this paper as [14]
Cites
Adaptive Fuzzy Systems and Control: Design and Stability Analysis
Wang, L. (1994) · Medical Entomology and Zoology · Cited by 2,736 · see citing works
Online actor–critic algorithm to solve the continuous-time infinite horizon optimal control problem
Vamvoudakis, K. G., & Lewis, F. L. (2010) · Automatica · doi:10.1016/j.automatica.2010.02.018 · Cited by 1,722 · see citing works
Bhasin, S., Kamalapurkar, R., Johnson, M. L., Vamvoudakis, K. G., Lewis, F. L., & Dixon, W. E. (2012) · Automatica · doi:10.1016/j.automatica.2012.09.019 · Cited by 646 · see citing works
Zhang, H., Cui, L., Zhang, X., & Luo, Y. (2011) · IEEE Transactions on Neural Networks · doi:10.1109/tnn.2011.2168538 · Cited by 645 · see citing works
Tong, S., Huo, B., & Li, Y. (2013) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2013.2241770 · Cited by 560 · see citing works
Self-citationObserver-based fuzzy adaptive control for strict-feedback nonlinear systems
Tong, S., & Li, Y. (2008) · Fuzzy Sets and Systems · doi:10.1016/j.fss.2008.09.004 · Cited by 463 · see citing works
Self-citationTong, S., Liu, C., & Li, Y. (2010) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2010.2050326 · Cited by 451 · see citing works
Self-citationAdaptive Fuzzy Control of a Class of Nonlinear Systems by Fuzzy Approximation Approach
Chen, B., Liu, X. P., Ge, S. S., & Lin, C. (2012) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2012.2190048 · Cited by 428 · see citing works
Zhang, H., Wei, Q., & Liu, D. (2010) · Automatica · doi:10.1016/j.automatica.2010.10.033 · Cited by 411 · see citing works
Liu, D., Wang, D., & Li, H. (2013) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2013.2280013 · Cited by 355 · see citing works
Liu, D., Wang, D., Wang, F., Li, H., & Yang, X. (2014) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2014.2357896 · Cited by 310 · see citing works
Chen, C. L. P., Ren, C., & Du, T. (2015) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2015.2486817 · Cited by 308 · see citing works
Decentralized adaptive control of nonlinear systems using radial basis neural networks
Spooner, J. T., & Passino, K. M. (1999) · IEEE Transactions on Automatic Control · doi:10.1109/9.802914 · Cited by 307 · see citing works
Zhou, Q. F., Shi, P., Liu, H., & Xu, S. (2012) · IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics) · doi:10.1109/tsmcb.2012.2196432 · Cited by 293 · see citing works
Wang, H., Liu, X., Liu, K., & Karimi, H. R. (2014) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2014.2375917 · Cited by 282 · see citing works
Fuzzy adaptive controller for MIMO nonlinear systems with known and unknown control direction
Boulkroune, A., Tadjine, M., M’Saad, M., & Farza, M. (2009) · Fuzzy Sets and Systems · doi:10.1016/j.fss.2009.04.011 · Cited by 258 · see citing works
Global Adaptive Dynamic Programming for Continuous-Time Nonlinear Systems
Jiang, Y., & Jiang, Z.-P. (2015) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2015.2414811 · Cited by 244 · see citing works
Wang, D., Liu, D., & Li, H. (2014) · IEEE Transactions on Automation Science and Engineering · doi:10.1109/tase.2013.2296206 · Cited by 238 · see citing works
1 Global Adaptive Dynamic Programming for Continuous-Time Nonlinear SystemsPreprint
Jiang, Y., Member, S., & Jiang, Z. (2016) · Cited by 235 · see citing works
Data-Based Adaptive Critic Designs for Nonlinear Robust Optimal Control With Uncertain Dynamics
Wang, D., Liu, D., Zhang, Q., et al. (2015) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2015.2492941 · Cited by 217 · see citing works
Adaptive Fuzzy Control of Nonlinear Systems in Pure Feedback Form Based on Input-to-State Stability
Zhang, T., Wen, H., & Zhu, Q. (2009) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2009.2036906 · Cited by 198 · see citing works
Yoo, S. J., & Park, J. B. (2009) · IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics) · doi:10.1109/tsmcb.2009.2016110 · Cited by 197 · see citing works
Decentralized adaptive output feedback design for large-scale nonlinear systems
Jain, S. K., & Khorrami, F. (1997) · IEEE Transactions on Automatic Control · doi:10.1109/9.580893 · Cited by 186 · see citing works
Optimal Control of Nonlinear Continuous-Time Systems in Strict-Feedback Form
Zargarzadeh, H., Dierks, T., & Jagannathan, S. (2015) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2015.2441712 · Cited by 168 · see citing works
Output Feedback Stabilization for Time-Delay Nonlinear Interconnected Systems Using Neural Networks
Hua, C., & Guan, X. (2008) · IEEE Transactions on Neural Networks · doi:10.1109/tnn.2007.912318 · Cited by 156 · see citing works
Event-Driven Adaptive Robust Control of Nonlinear Systems With Uncertainties Through NDP Strategy
Wang, D., Mu, C., He, H., & Liu, D. (2016) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2016.2592682 · Cited by 156 · see citing works
Adaptive Tracking Control for A Class of Nonlinear Systems With a Fuzzy Dead-Zone Input
Liu, Z., Wang, F., Zhang, Y., Chen, X., & Chen, C. L. P. (2014) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2014.2310491 · Cited by 150 · see citing works
Yoo, S. J., Park, J. B., & Choi, Y. H. (2008) · Automatica · doi:10.1016/j.automatica.2008.07.019 · Cited by 149 · see citing works
Lin, D., & Wang, X. (2010) · Fuzzy Sets and Systems · doi:10.1016/j.fss.2010.03.006 · Cited by 145 · see citing works
Adaptive Dynamic Programming for a Class of Complex-Valued Nonlinear Systems
Song, R., Xiao, W., Zhang, H., et al. (2014) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2014.2306201 · Cited by 145 · see citing works
Luo, B., Wu, H., & Li, H. (2014) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2014.2320744 · Cited by 139 · see citing works
Liu, D., Huang, Y., Wang, D., & Wei, Q. (2013) · International Journal of Control · doi:10.1080/00207179.2013.790562 · Cited by 138 · see citing works
Boulkroune, A., & M’Saad, M. (2011) · Fuzzy Sets and Systems · doi:10.1016/j.fss.2011.12.005 · Cited by 107 · see citing works
Han, S.-I., & Lee, J. M. (2013) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2013.2279543 · Cited by 97 · see citing works
Yang, X., Liu, D., & Wei, Q. (2014) · IET Control Theory and Applications · doi:10.1049/iet-cta.2014.0186 · Cited by 88 · see citing works
Wang, D., Li, C., Liu, D., & Mu, C. (2016) · Information Sciences · doi:10.1016/j.ins.2016.05.034 · Cited by 72 · see citing works
Zargarzadeh, H., Dierks, T., & Jagannathan, S. (2013) · International Journal of Adaptive Control and Signal Processing · doi:10.1002/acs.2432 · Cited by 61 · see citing works
Adaptive fuzzy control for uncertain interconnected time-delay systems
Hua, C., Guan, X., & Shi, P. J. (2005) · Fuzzy Sets and Systems · doi:10.1016/j.fss.2005.01.002 · Cited by 47 · see citing works
Wang, H., & Yang, G. (2015) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2015.2504380 · Cited by 45 · see citing works
Learning Error Feedback Design of Direct Adaptive Fuzzy Control Systems
Hsueh, Y., & Su, S. (2011) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2011.2178854 · Cited by 43 · see citing works
Some new results on stability of Takagi–Sugeno fuzzy Hopfield neural networks
Ahn, C. K. (2011) · Fuzzy Sets and Systems · doi:10.1016/j.fss.2011.05.010 · Cited by 43 · see citing works
Hamdy, M. N., Ramadan, A., & Abozalam, B. A. (2016) · Journal of Intelligent Manufacturing · doi:10.1007/s10845-016-1218-x · Cited by 23 · see citing works
Huang, Y., Xiao, D.-S., Chen, X., et al. (2010) · Fuzzy Sets and Systems · doi:10.1016/j.fss.2010.05.003 · Cited by 22 · see citing works
Adaptive fuzzy decentralized control for nonlinear large-scale systems based on high-gain observer
Tong, S., Ren, C., & Li, Y. (2011) · Science China Information Sciences · doi:10.1007/s11432-011-4404-7 · Cited by 18 · see citing works
Self-citation
Flagged first, then by citations
Cited by
Sorted by citations
Sun, J., Yi, J., & Pu, Z. (2022) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2021.3052610 · Cited by 184 · see citing works
Bai, W., Chen, D., Zhao, B., & D'Ariano, A. (2025) · IEEE Transactions on Intelligent Vehicles · doi:10.1109/tiv.2024.3458894 · Cited by 31 · see citing works
Fuzzy adaptive optimal control for nonlinear switched systems with actuator hysteresis
Sui, S., Tong, S., Chen, C. L. P., & Sun, K. (2019) · International Journal of Adaptive Control and Signal Processing · doi:10.1002/acs.2975 · Cited by 23 · see citing works
Self-citationSun, J., Zhang, M., Ma, L., Ding, S., & Yu, X. (2025) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2025.3597432 · Cited by 7 · see citing works
Neural Network-Aided Sampled-Data Control for a Class of Nonlinear Systems With Unknown Dynamics
Zhou, N., Yan, J., Xia, Y., Li, T., & Cheng, X. (2025) · IEEE Transactions on Circuits and Systems II: Express Briefs · doi:10.1109/tcsii.2025.3620235
- Authors
- Tong, S., Sun, K., & Sui, S.
- Affiliations
- Liaoning University of Technology (CN)
- Venue
- IEEE Transactions on Fuzzy Systems
- Published
- 2018-04
- Volume
- 26
- Issue
- 2
- Pages
- 569-584
- ISSN
- 1063-6706 (ISSN-L)
- 1941-0034
- OpenAlex
- W2603406422
- Cited by
- 551
- References
- 44
- Citations by year
- 2026: 38 · 2025: 74 · 2024: 82 · 2023: 80 · 2022: 58 · 2021: 66 · 2020: 65 · 2019: 44 · 2018: 37 · 2017: 7
- FWCI
- 31.43
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Fuzzy Systems (publishedVersion)
- Funders
- National Natural Science Foundation of China (61374113, 61573175, 61603167)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Adaptive Dynamic Programming Control
- Physical Sciences › Engineering › Control and Systems Engineering › Adaptive Control of Nonlinear Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Keywords
- adaptive fuzzy control, decentralized optimal control, large-scale nonlinear systems, strict-feedback systems, fuzzy observer, backstepping control, adaptive dynamic programming, feedforward and feedback control, unmeasured state estimation, unknown nonlinearities, cost function minimization, closed-loop boundedness
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
