Dear Amol Patil

Basically, the graph theory has been used to model the relationships among agents of the multi-agent or multi-robot system where the vertices of the graph correspond to the agents (robots), and the edges model the relation among those agents. The mathematics approach used for the edges represents the nature of the relationship or communication among agents. From this approach, a big area of theoretical and practical research is developed. I am attaching some links, books, and paper references that can be helpful to understand this area.

Books and Chapter books

• https://magnus.ece.gatech.edu/Papers/ROBOMAT07.pdf
• https://pdfs.semanticscholar.org/7208/0c14258cf8ca884329d50fdbe51790670b5a.pdf
• Mesbahi, Mehran, and Magnus Egerstedt. Graph-theoretic methods in multiagent networks. Vol. 33. Princeton University Press, 2010.
• Lewis, Frank L., Hongwei Zhang, Kristian Hengster-Movric, and Abhijit Das. Cooperative control of multi-agent systems: optimal and adaptive design approaches. Springer Science & Business Media, 2013.

Papers

• Y. Cao, W. Yu, W. Ren and G. Chen, "An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination," in IEEE Transactions on Industrial Informatics, vol. 9, no. 1, pp. 427-438, Feb. 2013, doi: 10.1109/TII.2012.2219061.
• S. Knorn, Z. Chen and R. H. Middleton, "Overview: Collective Control of Multiagent Systems," in IEEE Transactions on Control of Network Systems, vol. 3, no. 4, pp. 334-347, Dec. 2016, doi: 10.1109/TCNS.2015.2468991.
• Zuo, Zongyu, Qing-Long Han, Boda Ning, Xiaohua Ge, and Xian-Ming Zhang. "An overview of recent advances in fixed-time cooperative control of multiagent systems." IEEE Transactions on Industrial Informatics 14, no. 6 (2018): 2322-2334.
• Ding, Lei, Qing-Long Han, Xiaohua Ge, and Xian-Ming Zhang. "An overview of recent advances in event-triggered consensus of multiagent systems." IEEE transactions on cybernetics 48, no. 4 (2017): 1110-1123.
• Wang, Xiaoling, Housheng Su, Xiaofan Wang, and Guanrong Chen. "An overview of coordinated control for multi-agent systems subject to input saturation." Perspectives in Science 7 (2016): 133-139.
• Herrera, Manuel, Marco Pérez-Hernández, Ajith Kumar Parlikad, and Joaquín Izquierdo. "Multi-Agent Systems and Complex Networks: Review and Applications in Systems Engineering." Processes 8, no. 3 (2020): 312.

Dear Amol Patil,

Experience shows us that the methods of constructing an MAS are more and more subtle, we often seek to define the behavior of agents at the local level to obtain expected properties at the global level. Almost all of these methods are linked to the use of Markovian decision-making processes (MDP) to model the system, even if other solutions are currently advanced, which is why we have recourse to the state graph and the graph theory in general. Also the increased complexity of the systems imposes the use of the theory of graph during the construction of the MAS.

Fore more details and information about this subject, i suggest you to see links on topic.

https://ieeexplore.ieee.org/document/7737421

Article An overview of coordinated control for multi-agent systems s...

Article Multi-Agent Systems and Complex Networks: Review and Applica...

Conference Paper Multiagent Reinforcement Learning for Urban Traffic Control ...

Best regards

Dear Amol Patil

Basically, the graph theory has been used to model the relationships among agents of the multi-agent or multi-robot system where the vertices of the graph correspond to the agents (robots), and the edges model the relation among those agents. The mathematics approach used for the edges represents the nature of the relationship or communication among agents. From this approach, a big area of theoretical and practical research is developed. I am attaching some links, books, and paper references that can be helpful to understand this area.

Books and Chapter books

• https://magnus.ece.gatech.edu/Papers/ROBOMAT07.pdf
• https://pdfs.semanticscholar.org/7208/0c14258cf8ca884329d50fdbe51790670b5a.pdf
• Mesbahi, Mehran, and Magnus Egerstedt. Graph-theoretic methods in multiagent networks. Vol. 33. Princeton University Press, 2010.
• Lewis, Frank L., Hongwei Zhang, Kristian Hengster-Movric, and Abhijit Das. Cooperative control of multi-agent systems: optimal and adaptive design approaches. Springer Science & Business Media, 2013.

Papers

• Y. Cao, W. Yu, W. Ren and G. Chen, "An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination," in IEEE Transactions on Industrial Informatics, vol. 9, no. 1, pp. 427-438, Feb. 2013, doi: 10.1109/TII.2012.2219061.
• S. Knorn, Z. Chen and R. H. Middleton, "Overview: Collective Control of Multiagent Systems," in IEEE Transactions on Control of Network Systems, vol. 3, no. 4, pp. 334-347, Dec. 2016, doi: 10.1109/TCNS.2015.2468991.
• Zuo, Zongyu, Qing-Long Han, Boda Ning, Xiaohua Ge, and Xian-Ming Zhang. "An overview of recent advances in fixed-time cooperative control of multiagent systems." IEEE Transactions on Industrial Informatics 14, no. 6 (2018): 2322-2334.
• Ding, Lei, Qing-Long Han, Xiaohua Ge, and Xian-Ming Zhang. "An overview of recent advances in event-triggered consensus of multiagent systems." IEEE transactions on cybernetics 48, no. 4 (2017): 1110-1123.
• Wang, Xiaoling, Housheng Su, Xiaofan Wang, and Guanrong Chen. "An overview of coordinated control for multi-agent systems subject to input saturation." Perspectives in Science 7 (2016): 133-139.
• Herrera, Manuel, Marco Pérez-Hernández, Ajith Kumar Parlikad, and Joaquín Izquierdo. "Multi-Agent Systems and Complex Networks: Review and Applications in Systems Engineering." Processes 8, no. 3 (2020): 312.

Dear Amol Patil

Learning algorithms have been used with graph theory in MAS control. reinforcement learning algorithms are useful for information sharing between different agents of MAS. Next you can set your control task by classifying the information signals with the help of RL and Graph theory. Please see the following my paper as an example:

Consensus Performance of Traffic Management System for Cognitive Radio Network: An Agent Control Approach

• Conference Paper Consensus Performance of Traffic Management System for Cogni...