Neural network-based distributed fault estimation for multi-Area interconnected power systems with actuator faults and network constraints
With the growing reliance of multi-area interconnected power systems on communication networks for large-scale data transmission, sensing, and control, network constraints can impair transient performance. This work develops a unified distributed fault-estimation framework based on a radial basis function neural network (RBF-NN) for multi-area interconnected power systems, addressing both communication constraints and actuator faults. We construct an augmented system by integrating the fault dynamics into the system model, and a distributed observer is developed to simultaneously estimate the system states and fault dynamics. The unknown fault effect is approximated by a radial basis function neural network (RBF-NN). A projection-based adaptation law ensures bounded parameter estimation under modeling uncertainties. State and fault estimates are updated using quantized measurements transmitted over networked channels, maintaining accuracy despite time-varying delays and disturbances. Sufficient stability and performance conditions are established by Lyapunov analysis and LMI conditions, guaranteeing exponential stability of the observer error dynamics and prescribed performance bounds under bounded time-varying delays and quantization effects. A three-area case study is presented, and precise state and fault reconstruction are shown for nominal, delayed, faulted, and worst-case scenarios. The proposed scheme is compared with a quantized H∞ estimator under actuator faults, time-varying delays, and quantization. The peak deviations of |Δω|, |ΔPtie|, and |ΔPmech| are reduced approximately 33%, 50%, and 27%, respectively, while maintaining bounded system states and neural weights.
1. Benosman M. A survey of some recent results on nonlinear fault tolerant control. Math Probl Eng. 2010;2010(1):586169. https://doi.org/10.1155/2010/586169
2. Tran HM, Trinh H. Distributed functional observer based fault detection for interconnected time-delay systems. IEEE Syst J. 2017;13(1):940-951. https://doi.org/10.1109/JSYST.2017.2759257
3. Zhang ZH. Interval observer-based fault isolation for discrete-time fuzzy interconnected systems with unknown interconnections. IEEE Trans Cybern. 2017;47(9):2413-2424. https://doi.org/10.1109/TCYB.2017.2707462
4. Zhang K, Jiang B, Shi P. Distributed fault estimation observer design with adjustable parameters for a class of nonlinear interconnected systems. IEEE Trans Cybern. 2018;49(12):4219-4228. https://doi.org/10.1109/TCYB.2018.2860588
5. Yang H, Huang C, Jiang B, Polycarpou MM. Fault estimation and accommodation of interconnected systems: A separation principle. IEEE Trans Cybern. 2018;49(12):4103-4116. https://doi.org/10.1109/TCYB.2018.2857820
6. Xia J, Jiang B, Zhang K. Unknown input observerbased distributed fault estimation of discrete-time nonlinear interconnected systems. Int J Control Autom Syst. 2022;20(3):803-812. https://doi.org/10.1007/s12555-021-0082-4
7. Song X, Man J, Song S, Ahn CK. Finite-time fault estimation and tolerant control for nonlinear interconnected distributed parameter systems with Markovian switching channels. IEEE Trans Circuits Syst I Regul Pap. 2021;69(3):1347-1359. https://doi.org/10.1109/TCSI.2021.3129372
8. Mahmoud MS, Memon AM, Shi P. Observerbased fault-tolerant control for a class of nonlinear networked control systems. Int J Control. 2014;87(8):1707-1715. https://doi.org/10.1016/j.jfranklin.2010.01.007
9. Mao Z, Jiang B, Shi P. Observer-based faulttolerant control for a class of nonlinear networked control systems. J Franklin Inst. 2010;347(6):940-956. https://doi.org/10.1016/j.jfranklin.2010.01.007
10. Alanis AY, Alvarez JG, Sanchez OD, Hernandez HM, Valdivia-G A. Fault-tolerant closed-loop controller using online fault detection by neural networks. Machines. 2024;12(12):844. https://doi.org/10.3390/machines12120844
11. Stiefelmaier J, Böm M, Sawodny O, Tarín C. Parity space-based fault diagnosis in piecewise linear systems. IFAC-PapersOnLine. 2023;56(2):10868-10873. https://doi.org/10.1016/j.ifacol.2023.10.764
12. Benjemaa R, Khorchani N, Elhsoumi A, Abdelkrim MN. Fault detection based on the parity space approach for neutral time delay systems. In: Proceedings of the 2025 IEEE 22nd International Multi-Conference on Systems, Signals & Devices (SSD). IEEE; 2025:1-5. https://doi.org/10.1109/SSD64182.2025.10989971
13. Mahmoud MS, Alyazidi NM. Quantized H∞ estimator over communication networks for distributed generation units. IEEE Trans Syst Man Cybern Syst. 2017;50(3):1134-1146. https://doi.org/10.1109/TSMC.2017.2734167
14. Alyazidi NM, Al-Wajih YA, Mahmoud MS. Iterative learning control for load frequency in cyberattacked multi-area power systems. IEEE Access. 2023;11:95481-95492. https://doi.org/10.1109/ACCESS.2023.3309150
15. Thanh TV, Le CQ, Viet DT, Hieu NH, Le VD. Advanced frequency control strategy for power systems with high renewable energy penetration: A battery energy storage system approach. Int J Optim Control Theor Appl. 2025;15(4):625. https://doi.org/10.36922/IJOCTA025150076
16. Ouzaz M, El Assoudi A, Soulami J, El Yaagoubi EH. Simultaneous state and fault estimation for Takagi-Sugeno implicit models with Lipschitz constraints. Int J Optim Control Theor Appl. 2021;11(1):100-108. https://doi.org/10.11121/ijocta.01.2021.00877
17. Li X, Qin H, Han H, Wu X. Fault diagnosis and fault-tolerant control design for nonlinear networked systems: An interval type-2 TS fuzzy approach. IEEE Trans Autom Sci Eng. 2026. https://doi.org/10.1109/TASE.2026.3656456
18. Qiao MY, Chang XH, Park JH. Observer-based fault estimation and compensation control for nonlinear multi-delays systems with multi-source faults. IEEE Trans Autom Sci Eng. 2026;23:7587-7598. https://doi.org/10.1109/TASE.2026.3678544
19. Wu X, Li N, Zhang T, Ding D. Fault detection based on time-delay dependent H−/H∞ observers for linear discrete systems. IEEE Access. 2026. https://doi.org/10.1109/ACCESS.2026.3661489
20. Wu J, Geng Y, Wang J. Robust H∞ fault-tolerant control with mixed time-varying delays. Actuators. 2026;15(2):73. https://doi.org/10.3390/act15020073
21. Wang B, Wang Y, Zhang Z, Tang M, Vakil G, Yang T. Review of fault-tolerant permanent magnet synchronous machine design and control for future aircraft application. Chin J Electr Eng. 2025;11(2):165-187. https://doi.org/10.23919/CJEE.2025.000139
22. Jia F, Cao F, He X. Active fault-tolerant control against intermittent faults for state-constrained nonlinear systems. IEEE Trans Syst Man Cybern Syst. 2024;54(4):2389-2401. https://doi.org/10.1109/TSMC.2023.3344292
23. Chen P, Yu L, Zhang D. Event-triggered sliding mode control of power systems with communication delay and sensor faults. IEEE Trans Circuits Syst I Regul Pap. 2020;68(2):797-807. https://doi.org/10.1109/TCSI.2020.3035603.
24. Wang H, Li J, He C, Song C. Robust adaptive optimal fault-tolerant control scheme for multimachine power systems via the stabilizing twostage policy iteration framework. IEEE Trans Circuits Syst I Regul Pap. 2025. https://doi.org/10.1109/TASE.2025.3603734
25. Huang S, Xiong L, Zhou Y, Gao F, Jia Q, Li X, Li X, Wang Z, Khan MW. Robust distributed fixed-time fault-tolerant control for shipboard microgrids with actuator fault. IEEE Trans Transp Electrif. 2024;11(1):1791-1804. https://doi.org/10.1109/TTE.2024.3411289
26. Grande D, Peruffo A, Salavasidis G, Anderlini E, Fenucci D, Phillips AB, Kosmatopoulos EB, Thomas G. Passive fault-tolerant augmented neural Lyapunov control: A method to synthesise control functions for marine vehicles affected by actuators faults. Control Eng Pract. 2024;148:105935. https://doi.org/10.1016/j.conengprac.2024.105935
27. Saif AWA, Wang X, Yang F. New results on the observer-based H∞ control for uncertain nonlinear networked control systems with random packet losses. IEEE Access. 2019;7. https://doi.org/10.1109/ACCESS.2019.2900551
28. Liu Z, Li Y, Li L, Ma K, Yang Y. On the security and stability for wireless networked control systems with external attack and disturbances. Int J Robust Nonlinear Control. 2022. https://doi.org/10.1002/rnc.6260
29. Xu Z, Yang X, Li X, Lu J. Input-to-state stability of switched network control systems under unknown deception attacks. IEEE Trans Autom Sci En. 2024. https://doi.org/10.1109/TCYB.2024.3376695
30. Lin H, Dong J, Park JH. Observer-based H∞ fault-tolerant tracking control of multi-agent systems with nonideal communication links and external disturbances. IEEE Trans Autom Sci Eng. 2025;22:14096-14107. https://doi.org/10.1109/TASE.2025.3557951
31. Peng C, Yue D, Tian E, Gu Z. Observer-based fault detection for networked control systems with network quality of services. Appl Math Model. 2010;34:1653-1661. https://doi.org/10.1016/j.apm.2009.09.014
32. Mu Y, Zhang H, Yan Y, Xie X. Distributed observer-based robust fault estimation design for discrete-time interconnected systems with disturbances. IEEE Trans Cybern. 2023. https://doi.org/10.1109/TCYB.2022.3232531
33. Deng C, Wen C. Distributed resilient observerbased fault-tolerant control for heterogeneous multiagent systems under actuator faults and DoS attacks. IEEE Trans Control Netw Syst. 2020;7(3):1308-1318. https://doi.org/10.1109/TCNS.2020.2972601
34. Huang S, Ren J, Ma Z, Peng C, Su H. Distributed observer-based H∞ fault-tolerant control for DC microgrids with sensor fault. IEEE Trans Circuits Syst I Regul Pap. 2021;68(4):1659-1669. https://doi.org/10.1109/TCSI.2020.3048971
35. Sun HT, Chen X, Zhang Z, Ge X, Peng C. Datadriven event-triggered sliding mode secure control for autonomous vehicles under actuator attacks. IEEE Trans Cybern. 2024. https://doi.org/10.1109/TCYB.2024.3490656
36. Mu Y, Zhang H, Xi R, Gao Z. State and fault estimations for discrete-time TS fuzzy systems with sensor and actuator faults. IEEE Trans Circuits Syst II Express Briefs. 2021;68(10):3326-3330. https://doi.org/10.1109/TCSII.2021.3067708
37. Alyazidi NM, Mahmoud MS. L1 adaptive networked controller for islanded distributed generation systems in a microgrid. Int J Syst Sci. 2018;49(12):2507-2524. https://doi.org/10.1080/00207721.2018.1487093
38. Mahmoud MS. Estimator design for networked control systems with nonstationary packet dropouts. IMA J Math Control Inf. 2013;30(3):395-405. https://doi.org/10.1093/imamci/dns030
