Agents-based systems; Control of networks; Decentralized control; Distributed control; Network analysis and control; Agent-based systems; Decentralised control; Distributed-control; Eigenvalue and eigenfunctions; Network analysis and controls; Power system dynamics; Resource management; Signed networks; Task analysis; Control and Systems Engineering; Control and Optimization
Abstract :
[en] We propose a new decentralized design to control opinion patterns on signed networks of agents making decisions about two options and to switch the network from any opinion pattern to a new desired one. Our method relies on switching transformations, which switch the sign of an agent's opinion at a stable equilibrium by flipping the sign of the interactions with its neighbors. The global dynamical behavior of the switched network can be predicted rigorously when the original, and thus the switched, networks are structurally balanced. Structural balance ensures that the network dynamics are monotone, which makes the study of the basin of attraction of the various opinion patterns amenable to monotone systems theory. We illustrate the utility of the approach through scenarios motivated by multi-robot coordination and dynamic task allocation.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Bizyaeva, Anastasia ; Princeton University, Department Of Mechanical And Aerospace Engineering, Princeton, United States
Amorim, Giovanna; Princeton University, Department Of Mechanical And Aerospace Engineering, Princeton, United States
Santos, Maria ; Princeton University, Department Of Mechanical And Aerospace Engineering, Princeton, United States
Franci, Alessio ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Brain-Inspired Computing ; National Autonomous University Of Mexico, Department Of Mathematics, Mexico City, Mexico
Leonard, Naomi Ehrich ; Princeton University, Department Of Mechanical And Aerospace Engineering, Princeton, United States
Language :
English
Title :
Switching Transformations for Decentralized Control of Opinion Patterns in Signed Networks: Application to Dynamic Task Allocation
Publication date :
2022
Journal title :
IEEE Control Systems Letters
eISSN :
2475-1456
Publisher :
Institute of Electrical and Electronics Engineers Inc.
ONR - Office of Naval Research [US-VA] [US-VA] ARO - Army Research Office [US-WA] [US-WA] UNAM - Universidad Nacional Autónoma de México [MX] CONACYT - Consejo Nacional de Ciencia y Tecnología [MX] NSF - National Science Foundation [US-VA] [US-VA]
Funding text :
This work was supported in part by the Office of Naval Research (ONR) under Grant N00014-19-1-2556; in part by the Army Research Office (ARO) under Grant W911NF-18-1-0325; in part by DGAPA-UNAM PAPIIT under Grant IN102420; in part by the Consejo Nacional de Ciencia y Tecnología (Conacyt) under Grant A1-S-10610; and in part by NSF Graduate Research Fellowship under Grant DGE-2039656.
A. Bizyaeva, A. Franci, and N. E. Leonard, "Nonlinear opinion dynamics with tunable sensitivity, " IEEE Trans. Autom. Control, early access, Mar. 16, 2022. [Online]. Available: doi.org/10.1109/TAC.2022.3159527
R. Gray, A. Franci, V. Srivastava, and N. E. Leonard, "Multiagent decision-making dynamics inspired by honeybees, " IEEE Trans. Control Netw. Syst., vol. 5, no. 2, pp. 793-806, Jun. 2018.
A. Bizyaeva, A. Matthews, A. Franci, and N. E. Leonard, "Patterns of nonlinear opinion formation on networks, " in Proc. Amer. Control Conf., 2021, pp. 2739-2744.
A. Bizyaeva, T. Sorochkin, A. Franci, and N. E. Leonard, "Control of agreement and disagreement cascades with distributed inputs, " in Proc. IEEE Conf. Decis. Control, 2021, pp. 4994-4999.
C. Altafini, "Consensus problems on networks with antagonistic interactions, " IEEE Trans. Autom. Control, vol. 58, no. 4, pp. 935-946, Apr. 2013.
J. Liu, X. Chen, T. Başar, and M. A. Belabbas, "Exponential convergence of the discrete-and continuous-time Altafini models, " IEEE Trans. Autom. Control, vol. 62, no. 12, pp. 6168-6182, Dec. 2017.
A. Fontan and C. Altafini, "Multiequilibria analysis for a class of collective decision-making networked systems, " IEEE Trans. Control Netw. Syst., vol. 5, no. 4, pp. 1931-1940, Dec. 2018.
A. Fontan and C. Altafini, "The role of frustration in collective decision-making dynamical processes on multiagent signed networks, " 2021, arXiv:2105.11396.
L. Wang, Y. Hong, G. Shi, and C. Altafini, "A biased assimilation model on signed graphs, " in Proc. IEEE Conf. Decis. Control, 2020, pp. 494-499.
G. Strang, Introduction to Linear Algebra, 5th ed. Wellesley, MA, USA: Cambridge Press, 2016.
D. M. W. Leenaerts and W. M. G. Bokhoven, Piecewise Linear Modeling and Analysis. New York, NY, USA: Springer, 1998.
F. Miranda-Villatoro, F. Castaños, and A. Franci, "Equivalence of linear complementarity problems: Theory and application to nonsmooth bifurcations, " 2021, arXiv:2108.06917.
H. Khalil, Nonlinear Systems, 3rd ed. Upper Saddle River, NJ, USA: Prentice-Hall, 2000.
T. Zaslavsky, "Signed graphs, " Discr. Appl. Math., vol. 4, no. 1, pp. 47-74, 1982.
T. Zaslavsky, "Matrices in the theory of signed simple graphs, " in Proc. ICDM, 2010, pp. 207-229.
H. L. Smith, "Systems of ordinary differential equations which generate an order preserving flow. A survey of results, " SIAM Rev., vol. 30, no. 1, pp. 87-113, 1988.
J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, vol. 42. New York, NY, USA: Springer-Verlag, 2013.
A. Khamis, A. Hussein, and A. Elmogy, "Multi-robot task allocation: A review of the state-of-the-art, " in Cooperative Robots and Sensor Networks, A. Koubâa and J. Martínez-de Dios, Eds. Cham, Switzerland: Springer, 2015, pp. 31-51.
S. Park, Y. D. Zhong, and N. E. Leonard, "Multi-robot task allocation games in dynamically changing environments, " in Proc. IEEE Int. Conf. Robot. Autom. (ICRA), Xi'an, China, 2021, pp. 8678-8684.
G. Notomista and M. Egerstedt, "Persistification of robotic tasks, " IEEE Trans. Control Syst. Technol., vol. 29, no. 2, pp. 756-767, Mar. 2021.
K. Lerman, C. Jones, A. Galstyan, and M. J. Matarić, "Analysis of dynamic task allocation in multi-robot systems, " Int. J. Robot. Res., vol. 25, no. 3, pp. 225-241, 2006.
