Main Article Content
Abstract
Multi-robot cooperation, unmanned aerial vehicle (UAV) formation control, intelligent transport systems, and distributed sensor networks are just a few domains where multi-agent systems are crucial, as they require coordinated behavior to achieve common goals such as exploration, resource allocation, distributed sensing, and target tracking. This paper investigates various neural network configurations utilized in the NN-MPC framework for consensus control of multi-agent robotic systems. The NN-MPC control is applied to the consensus problem of a leader-follower multi-agent system, where agents coordinate to achieve collective behavior. In this approach, MPC is utilized to predict the future values of the control objective, which is optimized by minimizing a cost function with various neural network architectures. Different neural network configurations based on feed-forward, recurrent neural networks, Fitnet, and cascade networks are explored for the NN-MPC-based multi-agent systems. The analysis is performed through a simulation-based model of a quadrotor fleet system. Results show that the follower agents achieve consensus 60% faster than with RNN-MPC in comparison to the feedforward neural network, whereas the results are more effective when compared with the cascade network configuration-based MPC, where agents reach consensus 90% early if paired with suitable training structures. Overall, the article contributes to the recent topic of research on learning-based MPC of the multi-agent system in achieving consensus for the leader-follower strategy.
Keywords
Article Details
References
- K. M. Khalil, M. Abdel-Aziz, T. T. Nazmy and A. B. M. Salem, “Machine Learning Algorithms for Multi-Agent Systems,” Proceedings of the International Conference on Intelligent Information Processing, Security and Advanced Communication, pp. 1–5, Nov. 2015. https://doi.org/10.1145/2816839.2816925
- L. Canese, G. C. Cardarilli, L. Di Nunzio, R. Fazzolari, D. Giardino, M. Re and S. Spanò, “Multi-Agent Reinforcement Learning: A Review of Challenges and Applications,” Applied Sciences, vol. 11, no. 11, p. 4948, 2021.https://doi.org/10.3390/app11114948
- D. Q. Mayne, “Model Predictive Control: Recent Developments and Future Promise,” Automatica, vol. 50, no. 12, pp. 2967–2986, 2014. https://doi.org/10.1016/j.automatica.2014.10.128
- A. Norouzi, H. Heidarifar, H. Borhan, M. Shahbakhti and C. R. Koch, “Integrating Machine Learning and Model Predictive Control for Automotive Applications: A Review and Future Directions,” Engineering Applications of Artificial Intelligence, vol. 120, p. 105878, 2023. https://doi.org/10.1016/j.engappai.2023.105878
- B. Yi, P. Bender, F. Bonarens and C. Stiller, “Model Predictive Trajectory Planning for Automated Driving,” IEEE Transactions on Intelligent Vehicles, vol. 4, no. 1, pp. 24–38, 2018. https://doi.org/10.1109/TIV.2018.2886683
- P. Kumar, M. Karamta and A. Markana, “Dynamic State Estimation for Multi-Machine Power System Using WLS and EKF: A Comparative Study,” Proceedings of the 2019 IEEE 16th India Council International Conference (INDICON), pp. 1–4, Dec. 2019.https://doi.org/10.1109/INDICON47234.2019.9030371
- M. Anilkumar, N. Padhiyar and K. Moudgalya, “Multi-Objective Prioritized Control of a Semi-Batch Process with Multiple Feed and Multiple Products Using Economic MPC,” Proceedings of the 2018 Indian Control Conference (ICC), pp. 264–269, Jan. 2018. https://doi.org/10.1109/INDIANCC.2018.8307989
- A. Markana, N. Padhiyar and K. Moudgalya, “Multi-Criterion Control of a Bioprocess in Fed-Batch Reactor Using EKF Based Economic Model Predictive Control,” Chemical Engineering Research and Design, vol. 136, pp. 282–294, 2018. https://doi.org/10.1016/j.cherd.2018.05.032
- J. M. Maciejowski, Predictive Control: With Constraints. Harlow, U.K.: Prentice Hall, 2002. ISBN: 0201398230.
- A. Ashoori, B. Moshiri, A. Khaki-Sedigh and M. R. Bakhtiari, “Optimal Control of a Nonlinear Fed-Batch Fermentation Process Using Model Predictive Approach,” Journal of Process Control, vol. 19, no. 7, pp. 1162–1173, 2009. https://doi.org/10.1016/j.jprocont.2009.03.006
- Y. Bengio, “On the Challenge of Learning Complex Functions,” Progress in Brain Research, vol. 165, pp. 521–534, 2007. https://doi.org/10.1016/S0079-6123(06)65033-4
- H. C. Myung and Z. Z. Bien, “Design of the Fuzzy Multiobjective Controller Based on the Eligibility Method,” International Journal of Intelligent Systems, vol. 18, no. 5, pp. 509–528, 2003. https://doi.org/10.1002/int.10101
- L. Dubreuil-Vall, G. Ruffini and J. A. Camprodon, “Deep Learning Convolutional Neural Networks Discriminate Adult ADHD from Healthy Individuals on the Basis of Event-Related Spectral EEG,” Frontiers in Neuroscience, vol. 14, p. 251, 2020. https://doi.org/10.3389/fnins.2020.00251
- Y. Zhu, J. Wang, H. Li, C. Liu and W. M. Grill, “Adaptive Parameter Modulation of Deep Brain Stimulation Based on Improved Supervisory Algorithm,” Frontiers in Neuroscience, vol. 15, p. 750806, 2021. https://doi.org/10.3389/fnins.2021.750806
- S. Seyedzadeh, F. P. Rahimian, I. Glesk and M. Roper, “Machine Learning for Estimation of Building Energy Consumption and Performance: A Review,” Visualization in Engineering, vol. 6, no. 1, p. 5, 2018. https://doi.org/10.1186/s40327-018-0064-7
- Chaubey, P., Markana, A., Vyas, D.R. . “RNN-Based Model Predictive Control of Multi-agent System Using Switching Topologies.” Data Science and Applications. ICDSA 2023. Proceedings in Lecture Notes in Networks and Systems, vol 821. Springer, Singapore, pp157-168 (February 2024). https://doi.org/10.1007/978-981-99-7814-4_13
- R. Chen and S. Peng, “Leader-Follower Quasi-Consensus of Multi-Agent Systems with Packet Loss Using Event-Triggered Impulsive Control,” Mathematics, vol. 11, no. 13, p. 2969, 2023. https://doi.org/10.3390/math11132969
- Y. Zhi, Z. Zhao and M. Qi, “Event-Triggered Finite-Time Consensus Control of Leader–Follower Multi-Agent Systems with Unknown Velocities,” Transactions of the Institute of Measurement and Control, vol. 45, no. 13, pp. 2515–2525, 2023. https://doi.org/0.1177/01423312221140619
- Y. Wu, J. Ma, X. Chen, J. Sun and F. Zhao, “Fixed-Time Leader-Follower Consensus for Multi-Agent Systems Under Event-Triggered Mechanism,” in Proceedings of the Chinese Conference on Swarm Intelligence and Cooperative Control, pp. 275–284, Nov. 2023.
- https://doi.org/10.1007/978-981-97-3340-8_25
- Y. Kuriki and T. Namerikawa, “Formation Control with Collision Avoidance for a Multi-UAV System Using Decentralized MPC and Consensus-Based Control,” SICE Journal of Control, Measurement, and System Integration, vol. 8, no. 4, pp. 285–294, 2015 https://doi.org/10.9746/jcmsi.8.285
- S. Dubay and Y. J. Pan, “Distributed MPC Based Collision Avoidance Approach for Consensus of Multiple Quadcopters,” Proceedings of the 2018 IEEE 14th International Conference on Control and Automation (ICCA), pp. 155–160, June 2018. https://doi.org/10.1109/ICCA.2018.8444273
- N. Saeednia and A. Khayatian, “Reset MPC-Based Control for Consensus of Multiagent Systems,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2024. , https://doi.org/10.1109/TSMC.2024.3510092
- F. Muñoz, J. M. Valdovinos, J. S. Cervantes-Rojas, S. S. Cruz and A. M. Santana, “Leader–Follower Consensus Control for a Class of Nonlinear Multi-Agent Systems Using Dynamical Neural Networks,” Neurocomputing, vol. 561, p. 126888, 2023. https://doi.org/10.1016/j.neucom.2023.126888
- Z. Yang, S. Sosnowski, Q. Liu, J. Jiao, A. Lederer and S. Hirche, “Distributed Learning Consensus Control for Unknown Nonlinear Multi-Agent Systems Based on Gaussian Processes,” Proceedings of the 2021 60th IEEE Conference on Decision and Control (CDC), pp. 4406–4411, 2021 https://doi.org/0.1109/CDC45484.2021.9683522
- Z. Wang, Y. Gao, A. I. Rikos, N. Pang and Y. Ji, “Fixed-Relative-Switched Threshold Strategies for Consensus Tracking Control of Nonlinear Multiagent Systems,” Proceedings of the 2025 IEEE 19th International Conference on Control & Automation (ICCA), pp. 899–905, June 2025. https://doi.org/10.48550/arXiv.2411.19571
- M. Li, H. Liu, F. Xie and H. Huang, “Adaptive Distributed Control for Leader–Follower Formation Based on a Recurrent SAC Algorithm,” Electronics, vol. 13, no. 17, p. 3513, 2024. https://doi.org/10.3390/electronics13173513
- K. G. Dastidar, O. Caelen and M. Granitzer, “Machine Learning Methods for Credit Card Fraud Detection: A Survey,” IEEE Access, 2024. https://doi.org/10.1109/ACCESS.2024.3487298
- K. Aitken and S. Mihalas, “Neural Population Dynamics of Computing with Synaptic Modulations,” eLife, vol. 12, p. e83035, 2023. https://doi.org/10.7554/eLife.83035
- B. R. Floriano, A. N. Vargas, J. Y. Ishihara and H. C. Ferreira, “Neural-Network-Based Model Predictive Control for Consensus of Nonlinear Systems,” Engineering Applications of Artificial Intelligence, vol. 116, p. 105327, 2022. https://doi.org/10.1016/j.engappai.2022.105327
- W. Ren, R. W. Beard and E. M. Atkins, “Information Consensus in Multivehicle Cooperative Control,” IEEE Control Systems Magazine, vol. 27, no. 2, pp. 71–82, 2007. https://doi.org/10.1109/MCS.2007.338264
- T. Zhang and Y. U. Hui, “Average Consensus in Networks of Multi-Agent with Multiple Time-Varying Delays,” International Journal of Communications, Network and System Sciences, vol. 3, no. 2, pp. 196–203, 2010. http://dx.doi.org/10.4236/ijcns.2010.32028
- J. Gao, J. Li, H. Pan, Z. Wu, X. Yin and H. Wang, “Consensus via Event-Triggered Strategy of Nonlinear Multi-Agent Systems with Markovian Switching Topologies,” ISA Transactions, vol. 104, pp. 122–129, 2020. https://doi.org/10.1016/j.isatra.2019.11.013
References
K. M. Khalil, M. Abdel-Aziz, T. T. Nazmy and A. B. M. Salem, “Machine Learning Algorithms for Multi-Agent Systems,” Proceedings of the International Conference on Intelligent Information Processing, Security and Advanced Communication, pp. 1–5, Nov. 2015. https://doi.org/10.1145/2816839.2816925
L. Canese, G. C. Cardarilli, L. Di Nunzio, R. Fazzolari, D. Giardino, M. Re and S. Spanò, “Multi-Agent Reinforcement Learning: A Review of Challenges and Applications,” Applied Sciences, vol. 11, no. 11, p. 4948, 2021.https://doi.org/10.3390/app11114948
D. Q. Mayne, “Model Predictive Control: Recent Developments and Future Promise,” Automatica, vol. 50, no. 12, pp. 2967–2986, 2014. https://doi.org/10.1016/j.automatica.2014.10.128
A. Norouzi, H. Heidarifar, H. Borhan, M. Shahbakhti and C. R. Koch, “Integrating Machine Learning and Model Predictive Control for Automotive Applications: A Review and Future Directions,” Engineering Applications of Artificial Intelligence, vol. 120, p. 105878, 2023. https://doi.org/10.1016/j.engappai.2023.105878
B. Yi, P. Bender, F. Bonarens and C. Stiller, “Model Predictive Trajectory Planning for Automated Driving,” IEEE Transactions on Intelligent Vehicles, vol. 4, no. 1, pp. 24–38, 2018. https://doi.org/10.1109/TIV.2018.2886683
P. Kumar, M. Karamta and A. Markana, “Dynamic State Estimation for Multi-Machine Power System Using WLS and EKF: A Comparative Study,” Proceedings of the 2019 IEEE 16th India Council International Conference (INDICON), pp. 1–4, Dec. 2019.https://doi.org/10.1109/INDICON47234.2019.9030371
M. Anilkumar, N. Padhiyar and K. Moudgalya, “Multi-Objective Prioritized Control of a Semi-Batch Process with Multiple Feed and Multiple Products Using Economic MPC,” Proceedings of the 2018 Indian Control Conference (ICC), pp. 264–269, Jan. 2018. https://doi.org/10.1109/INDIANCC.2018.8307989
A. Markana, N. Padhiyar and K. Moudgalya, “Multi-Criterion Control of a Bioprocess in Fed-Batch Reactor Using EKF Based Economic Model Predictive Control,” Chemical Engineering Research and Design, vol. 136, pp. 282–294, 2018. https://doi.org/10.1016/j.cherd.2018.05.032
J. M. Maciejowski, Predictive Control: With Constraints. Harlow, U.K.: Prentice Hall, 2002. ISBN: 0201398230.
A. Ashoori, B. Moshiri, A. Khaki-Sedigh and M. R. Bakhtiari, “Optimal Control of a Nonlinear Fed-Batch Fermentation Process Using Model Predictive Approach,” Journal of Process Control, vol. 19, no. 7, pp. 1162–1173, 2009. https://doi.org/10.1016/j.jprocont.2009.03.006
Y. Bengio, “On the Challenge of Learning Complex Functions,” Progress in Brain Research, vol. 165, pp. 521–534, 2007. https://doi.org/10.1016/S0079-6123(06)65033-4
H. C. Myung and Z. Z. Bien, “Design of the Fuzzy Multiobjective Controller Based on the Eligibility Method,” International Journal of Intelligent Systems, vol. 18, no. 5, pp. 509–528, 2003. https://doi.org/10.1002/int.10101
L. Dubreuil-Vall, G. Ruffini and J. A. Camprodon, “Deep Learning Convolutional Neural Networks Discriminate Adult ADHD from Healthy Individuals on the Basis of Event-Related Spectral EEG,” Frontiers in Neuroscience, vol. 14, p. 251, 2020. https://doi.org/10.3389/fnins.2020.00251
Y. Zhu, J. Wang, H. Li, C. Liu and W. M. Grill, “Adaptive Parameter Modulation of Deep Brain Stimulation Based on Improved Supervisory Algorithm,” Frontiers in Neuroscience, vol. 15, p. 750806, 2021. https://doi.org/10.3389/fnins.2021.750806
S. Seyedzadeh, F. P. Rahimian, I. Glesk and M. Roper, “Machine Learning for Estimation of Building Energy Consumption and Performance: A Review,” Visualization in Engineering, vol. 6, no. 1, p. 5, 2018. https://doi.org/10.1186/s40327-018-0064-7
Chaubey, P., Markana, A., Vyas, D.R. . “RNN-Based Model Predictive Control of Multi-agent System Using Switching Topologies.” Data Science and Applications. ICDSA 2023. Proceedings in Lecture Notes in Networks and Systems, vol 821. Springer, Singapore, pp157-168 (February 2024). https://doi.org/10.1007/978-981-99-7814-4_13
R. Chen and S. Peng, “Leader-Follower Quasi-Consensus of Multi-Agent Systems with Packet Loss Using Event-Triggered Impulsive Control,” Mathematics, vol. 11, no. 13, p. 2969, 2023. https://doi.org/10.3390/math11132969
Y. Zhi, Z. Zhao and M. Qi, “Event-Triggered Finite-Time Consensus Control of Leader–Follower Multi-Agent Systems with Unknown Velocities,” Transactions of the Institute of Measurement and Control, vol. 45, no. 13, pp. 2515–2525, 2023. https://doi.org/0.1177/01423312221140619
Y. Wu, J. Ma, X. Chen, J. Sun and F. Zhao, “Fixed-Time Leader-Follower Consensus for Multi-Agent Systems Under Event-Triggered Mechanism,” in Proceedings of the Chinese Conference on Swarm Intelligence and Cooperative Control, pp. 275–284, Nov. 2023.
https://doi.org/10.1007/978-981-97-3340-8_25
Y. Kuriki and T. Namerikawa, “Formation Control with Collision Avoidance for a Multi-UAV System Using Decentralized MPC and Consensus-Based Control,” SICE Journal of Control, Measurement, and System Integration, vol. 8, no. 4, pp. 285–294, 2015 https://doi.org/10.9746/jcmsi.8.285
S. Dubay and Y. J. Pan, “Distributed MPC Based Collision Avoidance Approach for Consensus of Multiple Quadcopters,” Proceedings of the 2018 IEEE 14th International Conference on Control and Automation (ICCA), pp. 155–160, June 2018. https://doi.org/10.1109/ICCA.2018.8444273
N. Saeednia and A. Khayatian, “Reset MPC-Based Control for Consensus of Multiagent Systems,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2024. , https://doi.org/10.1109/TSMC.2024.3510092
F. Muñoz, J. M. Valdovinos, J. S. Cervantes-Rojas, S. S. Cruz and A. M. Santana, “Leader–Follower Consensus Control for a Class of Nonlinear Multi-Agent Systems Using Dynamical Neural Networks,” Neurocomputing, vol. 561, p. 126888, 2023. https://doi.org/10.1016/j.neucom.2023.126888
Z. Yang, S. Sosnowski, Q. Liu, J. Jiao, A. Lederer and S. Hirche, “Distributed Learning Consensus Control for Unknown Nonlinear Multi-Agent Systems Based on Gaussian Processes,” Proceedings of the 2021 60th IEEE Conference on Decision and Control (CDC), pp. 4406–4411, 2021 https://doi.org/0.1109/CDC45484.2021.9683522
Z. Wang, Y. Gao, A. I. Rikos, N. Pang and Y. Ji, “Fixed-Relative-Switched Threshold Strategies for Consensus Tracking Control of Nonlinear Multiagent Systems,” Proceedings of the 2025 IEEE 19th International Conference on Control & Automation (ICCA), pp. 899–905, June 2025. https://doi.org/10.48550/arXiv.2411.19571
M. Li, H. Liu, F. Xie and H. Huang, “Adaptive Distributed Control for Leader–Follower Formation Based on a Recurrent SAC Algorithm,” Electronics, vol. 13, no. 17, p. 3513, 2024. https://doi.org/10.3390/electronics13173513
K. G. Dastidar, O. Caelen and M. Granitzer, “Machine Learning Methods for Credit Card Fraud Detection: A Survey,” IEEE Access, 2024. https://doi.org/10.1109/ACCESS.2024.3487298
K. Aitken and S. Mihalas, “Neural Population Dynamics of Computing with Synaptic Modulations,” eLife, vol. 12, p. e83035, 2023. https://doi.org/10.7554/eLife.83035
B. R. Floriano, A. N. Vargas, J. Y. Ishihara and H. C. Ferreira, “Neural-Network-Based Model Predictive Control for Consensus of Nonlinear Systems,” Engineering Applications of Artificial Intelligence, vol. 116, p. 105327, 2022. https://doi.org/10.1016/j.engappai.2022.105327
W. Ren, R. W. Beard and E. M. Atkins, “Information Consensus in Multivehicle Cooperative Control,” IEEE Control Systems Magazine, vol. 27, no. 2, pp. 71–82, 2007. https://doi.org/10.1109/MCS.2007.338264
T. Zhang and Y. U. Hui, “Average Consensus in Networks of Multi-Agent with Multiple Time-Varying Delays,” International Journal of Communications, Network and System Sciences, vol. 3, no. 2, pp. 196–203, 2010. http://dx.doi.org/10.4236/ijcns.2010.32028
J. Gao, J. Li, H. Pan, Z. Wu, X. Yin and H. Wang, “Consensus via Event-Triggered Strategy of Nonlinear Multi-Agent Systems with Markovian Switching Topologies,” ISA Transactions, vol. 104, pp. 122–129, 2020. https://doi.org/10.1016/j.isatra.2019.11.013