Self-triggered optimal fault-tolerant control for saturated-inputs zero-sum game nonlinear systems via particle swarm optimization-based reinforcement learning
•In this paper, PSOA is used for the first time to solve the optimal ZSG control problem for nonlinear systems. The algorithm can compensate for faults negative effects while minimizing the cost function.•Different from previous works on ETC, the design of the STC strategy avoids continuous monitori...
Saved in:
| Published in: | Communications in nonlinear science & numerical simulation Vol. 153; p. 109512 |
|---|---|
| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier B.V
01.02.2026
|
| Subjects: | |
| ISSN: | 1007-5704 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | •In this paper, PSOA is used for the first time to solve the optimal ZSG control problem for nonlinear systems. The algorithm can compensate for faults negative effects while minimizing the cost function.•Different from previous works on ETC, the design of the STC strategy avoids continuous monitoring for trigger errors in this study. Moreover, a better compromise between system performance and communication load can be achieved.•The design of the STC is suitable for nonlinear systems with saturated-inputs, which not only adjusts trigger moments in real time to reduce computational burden, but also ensures that the system maintains stable operation and avoids over-excitation.
This paper proposes a self-triggered fault-tolerant optimal control scheme for zero-sum game nonlinear systems with saturated-inputs by using particle swarm optimization-based adaptive dynamic programming. First, a new self-triggered control strategy is proposed to equivalently convert a fault-optimal control problem into finding an optimal zero-sum game control scheme. Then, a saturated-inputs problem is solved by constructing a novel value function. In addition, a self-triggered condition is designed to reduce the communication bandwidth and energy consumption. And, the particle swarm optimization algorithm is used instead of gradient descent to find the optimal neural network weights. Finally, the effectiveness of the developed control scheme is demonstrated via simulation results. |
|---|---|
| AbstractList | •In this paper, PSOA is used for the first time to solve the optimal ZSG control problem for nonlinear systems. The algorithm can compensate for faults negative effects while minimizing the cost function.•Different from previous works on ETC, the design of the STC strategy avoids continuous monitoring for trigger errors in this study. Moreover, a better compromise between system performance and communication load can be achieved.•The design of the STC is suitable for nonlinear systems with saturated-inputs, which not only adjusts trigger moments in real time to reduce computational burden, but also ensures that the system maintains stable operation and avoids over-excitation.
This paper proposes a self-triggered fault-tolerant optimal control scheme for zero-sum game nonlinear systems with saturated-inputs by using particle swarm optimization-based adaptive dynamic programming. First, a new self-triggered control strategy is proposed to equivalently convert a fault-optimal control problem into finding an optimal zero-sum game control scheme. Then, a saturated-inputs problem is solved by constructing a novel value function. In addition, a self-triggered condition is designed to reduce the communication bandwidth and energy consumption. And, the particle swarm optimization algorithm is used instead of gradient descent to find the optimal neural network weights. Finally, the effectiveness of the developed control scheme is demonstrated via simulation results. |
| ArticleNumber | 109512 |
| Author | Xu, Ning Niu, Ben Zhao, Junzheng Zhang, Liang Zong, Guangdeng |
| Author_xml | – sequence: 1 givenname: Junzheng orcidid: 0009-0008-4456-1789 surname: Zhao fullname: Zhao, Junzheng email: zhaojunzheng_i@163.com organization: College of Control Science and Engineering, Bohai University, Jinzhou Liaoning, 121013, China – sequence: 2 givenname: Ben orcidid: 0000-0002-3680-5594 surname: Niu fullname: Niu, Ben email: niubensdnu@163.com organization: Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian Liaoning, 116024, China – sequence: 3 givenname: Ning orcidid: 0000-0002-0717-1713 surname: Xu fullname: Xu, Ning email: hpxuning@163.com organization: College of Information Science and Technology, Bohai University, Jinzhou, Liaoning 121013, China – sequence: 4 givenname: Guangdeng orcidid: 0000-0001-6498-5580 surname: Zong fullname: Zong, Guangdeng email: zgd@tiangong.edu.cn organization: School of Control Science and Engineering, Tiangong University, 399 binshuixi Road, Tianjin, 300387, China – sequence: 5 givenname: Liang orcidid: 0000-0002-1907-016X surname: Zhang fullname: Zhang, Liang email: md18638@126.com organization: College of Control Science and Engineering, Bohai University, Jinzhou Liaoning, 121013, China |
| BookMark | eNp9kDtOAzEQhl0EiSRwAhpfwMH7zhYUKOIlRaIgveW1xytHXntle4OSy3BVDEtNNaPR_A99K7SwzgJCdxndZDSr748bYYMNm5zmVbq0VZYv0DKjtCFVQ8trtArhSNNnW5VL9PUBRpHodd-DB4ndGPXADVZ8MpFEZ8BzG7FwNnqXzs7jwOPkeQRJtB2nGPAFvCNhGnDPB8CpjtEWeHo8hwhDwCfN8ch91MIADp_cD3OMvvConSUdDynZg7bJXsAAKdAkA6ttf4OuFDcBbv_mGh2enw67V7J_f3nbPe6JaLc5KRVtxLZOOxS0E6pWMs9L0QHwqpVl0XVFrrqCNyBbKepS0pYWWZVXtC2p4FCsUTHbCu9C8KDY6BMHf2YZZT9Y2ZH9YmU_WNmMNakeZhWkZicNngWhwQqQ2oOITDr9r_4bgsqMiw |
| Cites_doi | 10.1002/oca.3202 10.1016/j.automatica.2004.11.034 10.1109/9.310060 10.1109/TSMC.2024.3520600 10.1016/j.arcontrol.2018.09.001 10.1109/TFUZZ.2024.3352590 10.1109/TKDE.2025.3543225 10.1016/j.cnsns.2025.108804 10.1016/j.ins.2025.122396 10.1016/j.engappai.2025.110207 10.1016/j.cnsns.2025.109074 10.1016/j.ins.2024.121769 10.1007/s11071-024-10399-z 10.1016/j.neunet.2024.106880 10.1007/s11071-024-10234-5 10.1016/j.isatra.2024.09.018 10.1080/00423114.2024.2376658 10.1109/TEVC.2023.3345470 10.1016/j.jfranklin.2024.107360 10.1007/s10957-024-02572-6 10.1007/s10489-022-04348-9 10.1016/j.ins.2024.121782 10.1002/oca.3200 10.1016/j.neunet.2024.106952 10.1016/j.isatra.2024.02.009 10.1109/9.847729 10.1109/TSMC.2024.3450274 10.1109/JAS.2020.1003063 10.1109/TEVC.2023.3340678 10.1007/s10957-024-02490-7 10.1016/j.fss.2025.109567 10.1016/j.neucom.2024.127701 10.1007/s00521-024-09442-2 |
| ContentType | Journal Article |
| Copyright | 2025 Elsevier B.V. |
| Copyright_xml | – notice: 2025 Elsevier B.V. |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.cnsns.2025.109512 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences |
| ExternalDocumentID | 10_1016_j_cnsns_2025_109512 S1007570425009219 |
| GroupedDBID | --K --M -01 -0A -0I -0Y -SA -S~ .~1 0R~ 1B1 1RT 1~. 1~5 29F 4.4 457 4G. 5GY 5VR 5VS 7-5 71M 8P~ 92M 9D9 9DA 9DU AAEDT AAEDW AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AATTM AAXKI AAXUO AAYWO ABAOU ABFNM ABJNI ABMAC ABNEU ABWVN ABXDB ACDAQ ACFVG ACGFS ACLOT ACNNM ACRPL ACVFH ADBBV ADCNI ADEZE ADGUI ADMUD ADNMO ADTZH AEBSH AECPX AEIPS AEKER AENEX AEUPX AFJKZ AFPUW AFTJW AFUIB AGHFR AGQPQ AGUBO AGYEJ AHJVU AIEXJ AIGII AIGVJ AIIUN AIKHN AITUG AIVDX AKBMS AKRWK AKYEP ALMA_UNASSIGNED_HOLDINGS AMRAJ ANKPU APXCP ARUGR ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CAJEA CCEZO CCVFK CHBEP CS3 CUBFJ DU5 EBS EFJIC EFKBS EFLBG EJD EO8 EO9 EP2 EP3 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-Q GBLVA HVGLF HZ~ IHE J1W JJJVA JUIAU KOM M41 MHUIS MO0 N9A O-L O9- OAUVE OGIMB OZT P-8 P-9 P2P PC. Q-- Q-0 Q38 R2- ROL RPZ RT1 RT9 S.. SDF SDG SES SEW SPC SPCBC SPD SSQ SST SSZ T5K T8Q T8Y U1G U5K UHS ~G- ~HD ~LA AAYXX CITATION |
| ID | FETCH-LOGICAL-c982-4f07c86c98e30bcf6fd224cbeea59d43bb32fb3a7ed9dc64d090315250940cae3 |
| ISSN | 1007-5704 |
| IngestDate | Thu Nov 27 00:30:35 EST 2025 Sat Nov 29 17:08:03 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Self-triggered control Zero-sum games Saturated-inputs Optimal control Particle swarm optimization algorithm |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c982-4f07c86c98e30bcf6fd224cbeea59d43bb32fb3a7ed9dc64d090315250940cae3 |
| ORCID | 0000-0001-6498-5580 0009-0008-4456-1789 0000-0002-3680-5594 0000-0002-0717-1713 0000-0002-1907-016X |
| ParticipantIDs | crossref_primary_10_1016_j_cnsns_2025_109512 elsevier_sciencedirect_doi_10_1016_j_cnsns_2025_109512 |
| PublicationCentury | 2000 |
| PublicationDate | February 2026 2026-02-00 |
| PublicationDateYYYYMMDD | 2026-02-01 |
| PublicationDate_xml | – month: 02 year: 2026 text: February 2026 |
| PublicationDecade | 2020 |
| PublicationTitle | Communications in nonlinear science & numerical simulation |
| PublicationYear | 2026 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Yue, Xia, Zhang, Park, Xie (bib0028) 2025; 183 Zhang, Yin, Niu, Zhao, Zhao (bib0008) 2025; 718 Xiang, Li, Zou (bib0036) 2024 Wang, Wang, Ding, Ge, Zhu (bib0013) 2025; 63 Zhang, Zong, Niu, Zhao, Xu (bib0043) 2025; 519 Yang, Zhao (bib0044) 2020; 7 Zhao, Xu, Niu, Zhao, Alorfix (bib0034) 2025; 362 Liu, Xu, Li, Alharbi, Zhao (bib0006) 2025; 147 Zhou, Li, Sheng, Qi, Cong (bib0003) 2024; 588 Zhao, Lun, Zhang, Zhao, Rudas (bib0019) 2025 Wang, Gu, Mei, Hu (bib0011) 2024; 147 Zhang, Zhao, Zhang (bib0030) 2025; 145 Ning, Wang, Chen, Li (bib0032) 2025 Zhang, Lin, Zhang (bib0012) 2025 Xie, Li, Wang, Wang, Peng, Jalil (bib0020) 2025; 29 Zhang, Evans (bib0021) 1994; 39 Zhang, Chadli, Xiang (bib0042) 2024; 32 Dong, Zhu, An, Jiang, Ma (bib0014) 2025; 181 Yang, Zhan, Liu, Li, Zhang (bib0017) 2024; 28 Qin, Zhang, Shang, Zhang, Zhang (bib0004) 2023; 53 Baldi, Valmorbida, Papachristodoulou, Kosmatopoulos (bib0023) 2016 Liu, Xu, Wang, Zong, Zhao, Li (bib0041) 2025 Chaoui, Giri, Dion, M-Saad, Dugard (bib0022) 2000; 45 Sun, Trafalis (bib0001) 2025; 204 Wu (bib0015) 2025; 113 Liu, Li, Duan, Chu, Ma (bib0026) 2025; 46 Chen, Wu, Lopes, Wang, Gu, Zhu (bib0016) 2025 Peng, Cui, Zhou (bib0033) 2024; 36 Pachter, Weintraub (bib0002) 2024; 202 Song, Jiang, Zhang, Peng, Guo (bib0018) 2025 Song, Zuo, Tong (bib0031) 2025; 55 Zhang, Wang, Meng, Yan, Qin (bib0027) 2024; 155 Tang, Yang, Mu, Song (bib0035) 2024; 54 Guan, Li, Chen, Liang, Wang, Lu (bib0009) 2025; 37 Jiang, Liu (bib0037) 2018; 46 Wang, Jia, Niu, Pan, Cheng (bib0007) 2025 Li, Zeng, Dai, Suganthan (bib0010) 2025 Liu, Zhang, Zhao, Wang, Liu (bib0038) 2026; 510 Abu-Khalaf, Lewis (bib0024) 2005; 41 He, Wang, Tian, Precup (bib0025) 2025; 697 Wei, Niu, Zong, Zhao (bib0039) 2025; 113 Gao, Xu, Zong, Wang, Niu, Zhao (bib0005) 2025; 698 Zhang, Yin, Zhao, Liu, Wang (bib0040) 2025 Chen, Su (bib0029) 2025; 46 Qin (10.1016/j.cnsns.2025.109512_bib0004) 2023; 53 Wang (10.1016/j.cnsns.2025.109512_bib0013) 2025; 63 Zhao (10.1016/j.cnsns.2025.109512_bib0019) 2025 Li (10.1016/j.cnsns.2025.109512_bib0010) 2025 Yue (10.1016/j.cnsns.2025.109512_bib0028) 2025; 183 Chaoui (10.1016/j.cnsns.2025.109512_bib0022) 2000; 45 Baldi (10.1016/j.cnsns.2025.109512_bib0023) 2016 Zhao (10.1016/j.cnsns.2025.109512_bib0034) 2025; 362 Sun (10.1016/j.cnsns.2025.109512_bib0001) 2025; 204 Xiang (10.1016/j.cnsns.2025.109512_bib0036) 2024 Chen (10.1016/j.cnsns.2025.109512_bib0029) 2025; 46 Zhang (10.1016/j.cnsns.2025.109512_bib0012) 2025 Yang (10.1016/j.cnsns.2025.109512_bib0017) 2024; 28 Liu (10.1016/j.cnsns.2025.109512_bib0006) 2025; 147 Peng (10.1016/j.cnsns.2025.109512_bib0033) 2024; 36 Guan (10.1016/j.cnsns.2025.109512_bib0009) 2025; 37 Wei (10.1016/j.cnsns.2025.109512_bib0039) 2025; 113 Zhang (10.1016/j.cnsns.2025.109512_bib0043) 2025; 519 Liu (10.1016/j.cnsns.2025.109512_bib0041) 2025 Xie (10.1016/j.cnsns.2025.109512_bib0020) 2025; 29 Zhang (10.1016/j.cnsns.2025.109512_bib0008) 2025; 718 He (10.1016/j.cnsns.2025.109512_bib0025) 2025; 697 Yang (10.1016/j.cnsns.2025.109512_bib0044) 2020; 7 Ning (10.1016/j.cnsns.2025.109512_bib0032) 2025 Zhang (10.1016/j.cnsns.2025.109512_bib0042) 2024; 32 Gao (10.1016/j.cnsns.2025.109512_bib0005) 2025; 698 Dong (10.1016/j.cnsns.2025.109512_bib0014) 2025; 181 Zhang (10.1016/j.cnsns.2025.109512_bib0021) 1994; 39 Liu (10.1016/j.cnsns.2025.109512_bib0026) 2025; 46 Zhou (10.1016/j.cnsns.2025.109512_bib0003) 2024; 588 Wu (10.1016/j.cnsns.2025.109512_bib0015) 2025; 113 Zhang (10.1016/j.cnsns.2025.109512_bib0030) 2025; 145 Song (10.1016/j.cnsns.2025.109512_bib0031) 2025; 55 Jiang (10.1016/j.cnsns.2025.109512_bib0037) 2018; 46 Liu (10.1016/j.cnsns.2025.109512_bib0038) 2026; 510 Song (10.1016/j.cnsns.2025.109512_bib0018) 2025 Wang (10.1016/j.cnsns.2025.109512_bib0007) 2025 Zhang (10.1016/j.cnsns.2025.109512_bib0027) 2024; 155 Pachter (10.1016/j.cnsns.2025.109512_bib0002) 2024; 202 Abu-Khalaf (10.1016/j.cnsns.2025.109512_bib0024) 2005; 41 Zhang (10.1016/j.cnsns.2025.109512_bib0040) 2025 Chen (10.1016/j.cnsns.2025.109512_bib0016) 2025 Tang (10.1016/j.cnsns.2025.109512_bib0035) 2024; 54 Wang (10.1016/j.cnsns.2025.109512_bib0011) 2024; 147 |
| References_xml | – start-page: 1 year: 2024 end-page: 11 ident: bib0036 article-title: Event-triggered optimal control for a class of continuous-time switched nonlinear systems publication-title: IEEE Trans Autom Sci Eng – volume: 147 start-page: 163 year: 2024 end-page: 175 ident: bib0011 article-title: Output information-based intermittent optimal control for continuous-time nonlinear systems with unmatched uncertainties via adaptive dynamic programming publication-title: ISA Trans – volume: 36 start-page: 7007 year: 2024 end-page: 7023 ident: bib0033 article-title: Event-triggered self-learning-based tracking control for nonlinear constrained-input systems with uncertain disturbances publication-title: Neural Comput Appl – volume: 7 start-page: 575 year: 2020 end-page: 583 ident: bib0044 article-title: Optimal neuro-control strategy for nonlinear systems with asymmetric input constraints publication-title: IEEE/CAA J Autom Sin – volume: 46 start-page: 114 year: 2025 end-page: 134 ident: bib0029 article-title: Event-triggered optimal control based on prescribed performance for a two-link robotic manipulator publication-title: Optim Control Appl Methods – start-page: 1 year: 2025 end-page: 11 ident: bib0032 article-title: Neural network observer based adaptive trajectory tracking control strategy of unmanned surface vehicle with event-triggered mechanisms and signal quantization publication-title: IEEE Trans Emerging Top Comput Intell – year: 2025 ident: bib0041 article-title: Hierarchical non-singular terminal sliding mode control for constrained under-actuated nonlinear systems against sensor faults publication-title: Nonlinear Dyn – volume: 155 start-page: 309 year: 2024 end-page: 318 ident: bib0027 article-title: Adaptive critic design for safety-optimal FTC of unknown nonlinear systems with asymmetric constrained-input publication-title: ISA Trans – volume: 53 start-page: 17460 year: 2023 end-page: 17475 ident: bib0004 article-title: Adaptive optimal safety tracking control for multiplayer mixed zero-sum games of continuous-time systems publication-title: Appl Intell – volume: 28 start-page: 1867 year: 2024 end-page: 1881 ident: bib0017 article-title: Grid classification-based surrogate-assisted particle swarm optimization for expensive multiobjective optimization publication-title: IEEE Trans Evol Comput – volume: 183 year: 2025 ident: bib0028 article-title: Event-based adaptive fixed-time optimal control for saturated fault-tolerant nonlinear multiagent systems via reinforcement learning algorithm publication-title: Neural Netw – volume: 41 start-page: 779 year: 2005 end-page: 791 ident: bib0024 article-title: Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach publication-title: Automatica – volume: 55 start-page: 2302 year: 2025 end-page: 2311 ident: bib0031 article-title: Fuzzy optimal event-triggered control for dynamic positioning of unmanned surface vehicle publication-title: IEEE Trans Syst Man Cybern Syst – volume: 510 year: 2026 ident: bib0038 article-title: Observer-based reachable set synthesis for multi-agent systems: a sampling-based distributed event-triggered strategy publication-title: Appl Math Comput – volume: 519 year: 2025 ident: bib0043 article-title: Adaptive fuzzy dynamic event-triggered control for PDE-ODE cascaded systems with actuator failures publication-title: Fuzzy Sets Syst – start-page: 1 year: 2025 end-page: 14 ident: bib0010 article-title: Complementary learning subnetworks towards parameter-efficient class-incremental learning publication-title: IEEE Trans Knowl Data Eng – volume: 202 start-page: 1137 year: 2024 end-page: 1157 ident: bib0002 article-title: The synthesis of optimal control laws using isaacs? method for the solution of differential games publication-title: J Optim Theory Appl – start-page: 1 year: 2025 end-page: 19 ident: bib0016 article-title: Complex-order quantum-behaved particle swarm optimization with double jump-out strategy publication-title: IEEE Trans Emerging Top Comput Intell – volume: 697 year: 2025 ident: bib0025 article-title: Model-free global sliding mode control using adaptive fuzzy system under constrained input amplitude and rate for mechatronic systems subject to mismatched disturbances publication-title: Inf Sci – volume: 718 year: 2025 ident: bib0008 article-title: Bumpless transfer control and reachable set estimation for Markovian networked systems against dos attacks publication-title: Inf Sci – volume: 147 year: 2025 ident: bib0006 article-title: Zero-sum games-based optimal fault tolerant control for control-constrained multiplayer systems with external disturbances via adaptive dynamic programming publication-title: Commun Nonlinear Sci Numer Simul – volume: 113 start-page: 3453 year: 2025 end-page: 3483 ident: bib0015 article-title: Numerical optimal control for nonlinear dynamical systems involving mixed-valued inputs and joint probability path-constraints publication-title: Nonlinear Dyn – start-page: 1 year: 2025 end-page: 16 ident: bib0018 article-title: A surrogate-assisted multi-phase ensemble feature selection algorithm with particle swarm optimization in imbalanced data publication-title: IEEE Trans Emerging Top Comput Intell – start-page: 5734 year: 2016 end-page: 5739 ident: bib0023 article-title: Online policy iterations for optimal control of input-saturated systems publication-title: 2016 American control conference (ACC) – volume: 32 start-page: 2403 year: 2024 end-page: 2412 ident: bib0042 article-title: Prescribed-time adaptive fuzzy optimal control for nonlinear systems publication-title: IEEE Trans Fuzzy Syst – volume: 39 start-page: 1718 year: 1994 end-page: 1722 ident: bib0021 article-title: Continuous direct adaptive control with saturation input constraint publication-title: IEEE Trans Automat Contr – volume: 63 start-page: 50 year: 2025 end-page: 70 ident: bib0013 article-title: Dynamic event-based cooperative control of virtually coupled high-speed trains: an ADP-based optimal control scheme publication-title: Veh Syst Dyn – start-page: 1 year: 2025 end-page: 13 ident: bib0012 article-title: PMGDA: A Preference-Based Multiple Gradient Descent Algorithm publication-title: IEEE Trans Emerg Top Comput Intell – year: 2025 ident: bib0040 article-title: Improved reachable set synthesis and asynchronous quantized control for switched fuzzy systems under dos attacks via dynamic event-triggered mechanism publication-title: Fuzzy Sets Syst – volume: 145 year: 2025 ident: bib0030 article-title: Event-triggered neuro-optimal fault tolerant control for uncertain macro–micro composite stage system with actuator faults publication-title: Eng Appl Artif Intell – volume: 54 start-page: 7117 year: 2024 end-page: 7128 ident: bib0035 article-title: Intermittent feedback optimal control of saturated-input nonlinear systems via adaptive dynamic programming publication-title: IEEE Trans Syst Man Cybern Syst – volume: 588 year: 2024 ident: bib0003 article-title: Optimal control strategies and target selection in multi-pursuer multi-evader differential games publication-title: Neurocomputing – volume: 362 year: 2025 ident: bib0034 article-title: Dynamic event-triggered optimal control for stochastic interconnected nonlinear systems with matched disturbances via adaptive dynamic programming publication-title: J Franklin Inst – volume: 37 start-page: 2831 year: 2025 end-page: 2845 ident: bib0009 article-title: PipeOptim: Ensuring Effective 1F1B Schedule With Optimizer-Dependent Weight Prediction publication-title: IEEE Trans Knowl Data Eng – volume: 29 start-page: 31 year: 2025 end-page: 45 ident: bib0020 article-title: A tractive population-assisted dual-population and two-phase evolutionary algorithm for constrained multiobjective optimization publication-title: IEEE Trans Evol Comput – year: 2025 ident: bib0007 article-title: Optimal damping factors explored for eliminating nonphysical attraction forces from viscous contact models used in cohesionless granular system publication-title: Commun Nonlinear Sci Numer Simul – start-page: 1 year: 2025 end-page: 11 ident: bib0019 article-title: Composite anti-disturbance control for networked systems with disturbances and actuator attacks via event-triggered output feedback publication-title: IEEE Trans Cybern – volume: 698 year: 2025 ident: bib0005 article-title: Fuzzy weight-based secure formation control for two-order heterogeneous multi-agent systems via reinforcement learning publication-title: Inf Sci – volume: 46 start-page: 135 year: 2025 end-page: 154 ident: bib0026 article-title: Experience replay based online adaptive robust tracking control for partially unknown nonlinear systems with asymmetric constrained-input publication-title: Optim Control Appl Methods – volume: 113 start-page: 729 year: 2025 end-page: 749 ident: bib0039 article-title: Adaptive neural self-triggered bipartite consensus control for nonlinear fractional-order multi-agent systems with actuator fault publication-title: Nonlinear Dyn – volume: 204 start-page: 40 year: 2025 ident: bib0001 article-title: -optimal control via game-theoretic differential dynamic programming and Gaussian processes publication-title: J Optim Theory Appl – volume: 45 start-page: 485 year: 2000 end-page: 490 ident: bib0022 article-title: Direct adaptive control subject to input amplitude constraint publication-title: IEEE Trans Autom Control – volume: 46 start-page: 58 year: 2018 end-page: 79 ident: bib0037 article-title: Small-gain theory for stability and control of dynamical networks: a survey publication-title: Annu Rev Control – volume: 181 year: 2025 ident: bib0014 article-title: Barrier-critic-disturbance approximate optimal control of nonzero-sum differential games for modular robot manipulators publication-title: Neural Netw – volume: 519 issue: 1 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0043 article-title: Adaptive fuzzy dynamic event-triggered control for PDE-ODE cascaded systems with actuator failures publication-title: Fuzzy Sets Syst – start-page: 5734 year: 2016 ident: 10.1016/j.cnsns.2025.109512_bib0023 article-title: Online policy iterations for optimal control of input-saturated systems – start-page: 1 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0032 article-title: Neural network observer based adaptive trajectory tracking control strategy of unmanned surface vehicle with event-triggered mechanisms and signal quantization publication-title: IEEE Trans Emerging Top Comput Intell – volume: 46 start-page: 135 issue: 1 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0026 article-title: Experience replay based online adaptive robust tracking control for partially unknown nonlinear systems with asymmetric constrained-input publication-title: Optim Control Appl Methods doi: 10.1002/oca.3202 – year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0041 article-title: Hierarchical non-singular terminal sliding mode control for constrained under-actuated nonlinear systems against sensor faults publication-title: Nonlinear Dyn – volume: 41 start-page: 779 issue: 5 year: 2005 ident: 10.1016/j.cnsns.2025.109512_bib0024 article-title: Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach publication-title: Automatica doi: 10.1016/j.automatica.2004.11.034 – volume: 39 start-page: 1718 issue: 8 year: 1994 ident: 10.1016/j.cnsns.2025.109512_bib0021 article-title: Continuous direct adaptive control with saturation input constraint publication-title: IEEE Trans Automat Contr doi: 10.1109/9.310060 – volume: 55 start-page: 2302 issue: 3 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0031 article-title: Fuzzy optimal event-triggered control for dynamic positioning of unmanned surface vehicle publication-title: IEEE Trans Syst Man Cybern Syst doi: 10.1109/TSMC.2024.3520600 – volume: 46 start-page: 58 year: 2018 ident: 10.1016/j.cnsns.2025.109512_bib0037 article-title: Small-gain theory for stability and control of dynamical networks: a survey publication-title: Annu Rev Control doi: 10.1016/j.arcontrol.2018.09.001 – volume: 32 start-page: 2403 issue: 4 year: 2024 ident: 10.1016/j.cnsns.2025.109512_bib0042 article-title: Prescribed-time adaptive fuzzy optimal control for nonlinear systems publication-title: IEEE Trans Fuzzy Syst doi: 10.1109/TFUZZ.2024.3352590 – volume: 37 start-page: 2831 issue: 5 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0009 article-title: PipeOptim: Ensuring Effective 1F1B Schedule With Optimizer-Dependent Weight Prediction publication-title: IEEE Trans Knowl Data Eng doi: 10.1109/TKDE.2025.3543225 – volume: 147 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0006 article-title: Zero-sum games-based optimal fault tolerant control for control-constrained multiplayer systems with external disturbances via adaptive dynamic programming publication-title: Commun Nonlinear Sci Numer Simul doi: 10.1016/j.cnsns.2025.108804 – start-page: 1 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0010 article-title: Complementary learning subnetworks towards parameter-efficient class-incremental learning publication-title: IEEE Trans Knowl Data Eng – volume: 718 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0008 article-title: Bumpless transfer control and reachable set estimation for Markovian networked systems against dos attacks publication-title: Inf Sci doi: 10.1016/j.ins.2025.122396 – volume: 145 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0030 article-title: Event-triggered neuro-optimal fault tolerant control for uncertain macro–micro composite stage system with actuator faults publication-title: Eng Appl Artif Intell doi: 10.1016/j.engappai.2025.110207 – year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0007 article-title: Optimal damping factors explored for eliminating nonphysical attraction forces from viscous contact models used in cohesionless granular system publication-title: Commun Nonlinear Sci Numer Simul doi: 10.1016/j.cnsns.2025.109074 – volume: 697 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0025 article-title: Model-free global sliding mode control using adaptive fuzzy system under constrained input amplitude and rate for mechatronic systems subject to mismatched disturbances publication-title: Inf Sci doi: 10.1016/j.ins.2024.121769 – volume: 113 start-page: 3453 issue: 4 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0015 article-title: Numerical optimal control for nonlinear dynamical systems involving mixed-valued inputs and joint probability path-constraints publication-title: Nonlinear Dyn doi: 10.1007/s11071-024-10399-z – volume: 181 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0014 article-title: Barrier-critic-disturbance approximate optimal control of nonzero-sum differential games for modular robot manipulators publication-title: Neural Netw doi: 10.1016/j.neunet.2024.106880 – volume: 113 start-page: 729 issue: 1 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0039 article-title: Adaptive neural self-triggered bipartite consensus control for nonlinear fractional-order multi-agent systems with actuator fault publication-title: Nonlinear Dyn doi: 10.1007/s11071-024-10234-5 – volume: 155 start-page: 309 year: 2024 ident: 10.1016/j.cnsns.2025.109512_bib0027 article-title: Adaptive critic design for safety-optimal FTC of unknown nonlinear systems with asymmetric constrained-input publication-title: ISA Trans doi: 10.1016/j.isatra.2024.09.018 – start-page: 1 year: 2024 ident: 10.1016/j.cnsns.2025.109512_bib0036 article-title: Event-triggered optimal control for a class of continuous-time switched nonlinear systems publication-title: IEEE Trans Autom Sci Eng – volume: 63 start-page: 50 issue: 1 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0013 article-title: Dynamic event-based cooperative control of virtually coupled high-speed trains: an ADP-based optimal control scheme publication-title: Veh Syst Dyn doi: 10.1080/00423114.2024.2376658 – volume: 29 start-page: 31 issue: 1 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0020 article-title: A tractive population-assisted dual-population and two-phase evolutionary algorithm for constrained multiobjective optimization publication-title: IEEE Trans Evol Comput doi: 10.1109/TEVC.2023.3345470 – volume: 362 issue: 2 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0034 article-title: Dynamic event-triggered optimal control for stochastic interconnected nonlinear systems with matched disturbances via adaptive dynamic programming publication-title: J Franklin Inst doi: 10.1016/j.jfranklin.2024.107360 – start-page: 1 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0019 article-title: Composite anti-disturbance control for networked systems with disturbances and actuator attacks via event-triggered output feedback publication-title: IEEE Trans Cybern – volume: 204 start-page: 40 issue: 3 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0001 article-title: h∞-optimal control via game-theoretic differential dynamic programming and Gaussian processes publication-title: J Optim Theory Appl doi: 10.1007/s10957-024-02572-6 – volume: 53 start-page: 17460 issue: 14 year: 2023 ident: 10.1016/j.cnsns.2025.109512_bib0004 article-title: Adaptive optimal safety tracking control for multiplayer mixed zero-sum games of continuous-time systems publication-title: Appl Intell doi: 10.1007/s10489-022-04348-9 – volume: 698 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0005 article-title: Fuzzy weight-based secure formation control for two-order heterogeneous multi-agent systems via reinforcement learning publication-title: Inf Sci doi: 10.1016/j.ins.2024.121782 – volume: 46 start-page: 114 issue: 1 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0029 article-title: Event-triggered optimal control based on prescribed performance for a two-link robotic manipulator publication-title: Optim Control Appl Methods doi: 10.1002/oca.3200 – volume: 183 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0028 article-title: Event-based adaptive fixed-time optimal control for saturated fault-tolerant nonlinear multiagent systems via reinforcement learning algorithm publication-title: Neural Netw doi: 10.1016/j.neunet.2024.106952 – volume: 147 start-page: 163 year: 2024 ident: 10.1016/j.cnsns.2025.109512_bib0011 article-title: Output information-based intermittent optimal control for continuous-time nonlinear systems with unmatched uncertainties via adaptive dynamic programming publication-title: ISA Trans doi: 10.1016/j.isatra.2024.02.009 – volume: 45 start-page: 485 issue: 3 year: 2000 ident: 10.1016/j.cnsns.2025.109512_bib0022 article-title: Direct adaptive control subject to input amplitude constraint publication-title: IEEE Trans Autom Control doi: 10.1109/9.847729 – volume: 54 start-page: 7117 issue: 11 year: 2024 ident: 10.1016/j.cnsns.2025.109512_bib0035 article-title: Intermittent feedback optimal control of saturated-input nonlinear systems via adaptive dynamic programming publication-title: IEEE Trans Syst Man Cybern Syst doi: 10.1109/TSMC.2024.3450274 – volume: 7 start-page: 575 issue: 2 year: 2020 ident: 10.1016/j.cnsns.2025.109512_bib0044 article-title: Optimal neuro-control strategy for nonlinear systems with asymmetric input constraints publication-title: IEEE/CAA J Autom Sin doi: 10.1109/JAS.2020.1003063 – start-page: 1 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0012 article-title: PMGDA: A Preference-Based Multiple Gradient Descent Algorithm publication-title: IEEE Trans Emerg Top Comput Intell – volume: 28 start-page: 1867 issue: 6 year: 2024 ident: 10.1016/j.cnsns.2025.109512_bib0017 article-title: Grid classification-based surrogate-assisted particle swarm optimization for expensive multiobjective optimization publication-title: IEEE Trans Evol Comput doi: 10.1109/TEVC.2023.3340678 – start-page: 1 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0018 article-title: A surrogate-assisted multi-phase ensemble feature selection algorithm with particle swarm optimization in imbalanced data publication-title: IEEE Trans Emerging Top Comput Intell – start-page: 1 year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0016 article-title: Complex-order quantum-behaved particle swarm optimization with double jump-out strategy publication-title: IEEE Trans Emerging Top Comput Intell – volume: 202 start-page: 1137 issue: 3 year: 2024 ident: 10.1016/j.cnsns.2025.109512_bib0002 article-title: The synthesis of optimal control laws using isaacs? method for the solution of differential games publication-title: J Optim Theory Appl doi: 10.1007/s10957-024-02490-7 – year: 2025 ident: 10.1016/j.cnsns.2025.109512_bib0040 article-title: Improved reachable set synthesis and asynchronous quantized control for switched fuzzy systems under dos attacks via dynamic event-triggered mechanism publication-title: Fuzzy Sets Syst doi: 10.1016/j.fss.2025.109567 – volume: 510 year: 2026 ident: 10.1016/j.cnsns.2025.109512_bib0038 article-title: Observer-based reachable set synthesis for multi-agent systems: a sampling-based distributed event-triggered strategy publication-title: Appl Math Comput – volume: 588 year: 2024 ident: 10.1016/j.cnsns.2025.109512_bib0003 article-title: Optimal control strategies and target selection in multi-pursuer multi-evader differential games publication-title: Neurocomputing doi: 10.1016/j.neucom.2024.127701 – volume: 36 start-page: 7007 issue: 13 year: 2024 ident: 10.1016/j.cnsns.2025.109512_bib0033 article-title: Event-triggered self-learning-based tracking control for nonlinear constrained-input systems with uncertain disturbances publication-title: Neural Comput Appl doi: 10.1007/s00521-024-09442-2 |
| SSID | ssj0016954 |
| Score | 2.4510338 |
| Snippet | •In this paper, PSOA is used for the first time to solve the optimal ZSG control problem for nonlinear systems. The algorithm can compensate for faults... |
| SourceID | crossref elsevier |
| SourceType | Index Database Publisher |
| StartPage | 109512 |
| SubjectTerms | Optimal control Particle swarm optimization algorithm Saturated-inputs Self-triggered control Zero-sum games |
| Title | Self-triggered optimal fault-tolerant control for saturated-inputs zero-sum game nonlinear systems via particle swarm optimization-based reinforcement learning |
| URI | https://dx.doi.org/10.1016/j.cnsns.2025.109512 |
| Volume | 153 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 issn: 1007-5704 databaseCode: AIEXJ dateStart: 19960101 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://www.sciencedirect.com omitProxy: false ssIdentifier: ssj0016954 providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtZ3Nb9MwFMCtsnHgwjdifMkHbsHT5sRJfJzQEHCYkOih4hI5jl06pWnVJGXaP8P_xV_Dc2ynyTZN7MAliqrEtvp-sZ-f3wdC72lcpKkOKRFc5ySKNSM8FymJuWaaRomWTHTFJpKzs3Q2498mkz8-FmZbJlWVXlzw9X8VNfwGwjahs3cQd98o_AD3IHS4gtjh-k-C_65KTRrYdM9NGc5gBXPC0kQpirZsSLMqFaxOTe-ibrwMa5PcE3TOgiyqddvUwaXarAiMOZiLpQoqm01D-LTPdbBdiGDtug7qX2KztN24mE5ilkYTFdNlZZWdAdKXp5gPteFRdErnmDvoy006Bs2qtedKZVAvlq7e2MDibQ-P2uryp3LtdwctbcfuLtRt1lr0d8_8cP7I8J1U88K_7GwgtHeb7qdtY3BliS1k3M_rLBzMzMdGl6Q3LhrWfnF-KKu6MhncKTvcPT1O0X1l6ewdGr2v3HnWNZKZRjLbyD20TxPGYcbdP_lyOvvan3HFvKvR14_d58TqvA-vjeVmvWmgC00fo4duE4NPLAFP0ERVT9Ejt6HBbrmon6HfYxaxYxGPWcSORQyw4KssYs8iNizing_sWMTAIvYs4o5FfJ1FPGIRexafo-mn0-nHz8RVBCGSw04w0keJTGO4V-FRLnWsC9BAZa6UYLyIwjwPqc5DkaiCFzKOCmOENAW-TJJIKVT4Au3BONVLhCVLw0JyLQsGCq6AZSuhQjMRy5wd5yk9QB_8352tbd6X7BYhH6DYiyRz34dVSTOA7LYXX92tn9fowY7_N2iv2bTqLbovt82i3rxzhP0FoEzJtA |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Self-triggered+optimal+fault-tolerant+control+for+saturated-inputs+zero-sum+game+nonlinear+systems+via+particle+swarm+optimization-based+reinforcement+learning&rft.jtitle=Communications+in+nonlinear+science+%26+numerical+simulation&rft.au=Zhao%2C+Junzheng&rft.au=Niu%2C+Ben&rft.au=Xu%2C+Ning&rft.au=Zong%2C+Guangdeng&rft.date=2026-02-01&rft.issn=1007-5704&rft.volume=153&rft.spage=109512&rft_id=info:doi/10.1016%2Fj.cnsns.2025.109512&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_cnsns_2025_109512 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1007-5704&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1007-5704&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1007-5704&client=summon |