×

A new look at distributed optimal output agreement of multi-agent systems. (English) Zbl 1480.93024

Summary: This paper studies the distributed optimal output agreement problem for multi-agent systems with the agents admitting the essential reference-tracking capability characterized by the well-known notion of system types. In the present system setup, the agents know only the gradient values of their corresponding local objective functions, and distributed optimizers are designed to generate reference signals for the agents. Under mild assumptions on the local objective functions and the connectivity between the agents, it is shown that the agents’ outputs can be steered to the global optimum of the total objective function as long as the system type of each agent is not less than one. A numerical example on the simultaneous formation and source seeking of a group of vertical take-off and landing (VTOL) vehicles is employed to verify the effectiveness of the proposed approach.

MSC:

93A16 Multi-agent systems
68W15 Distributed algorithms
Full Text: DOI

References:

[1] Abdessameud, A.; Tayebi, A., Distributed output regulation of heterogeneous linear multi-agent systems with communication constraints, Automatica, 91, 152-158 (2018) · Zbl 1387.93007
[2] Bai, H.; Arcak, M.; Wen, J., Cooperative control design: A systematic, passivity-based approach (2011), Springer · Zbl 1228.93001
[3] Bayat, B.; Crasta, N.; Crespi, A.; Pascoal, A. M.; Ijspeert, A., Environmental monitoring using autonomous vehicles: a survey of recent searching techniques, Current Opinion in Biotechnology, 45, 76-84 (2017)
[4] Bertsekas, D.; Tsitsiklis, J., Parallel and distributed computation: Numerical methods (1989), Prentice-Hall · Zbl 0743.65107
[5] Bhattacharya, S.; Kumar, V.; Likhachev, M., Distituted optimization with pairwise constraints and its application to multi-robot path planning, Robotics: Science and Systems VI, 177 (2011)
[6] Briñón-Arranz, L.; Renzaglia, A.; Schenato, L., Multirobot symmetric formations for gradient and hessian estimation with application to source seeking, IEEE Transactions on Robotics, 35, 782-789 (2019)
[7] Bullo, F.; Cortes, J.; Martinez, S., Distributed control of robotic networks (2009), Princeton · Zbl 1193.93137
[8] Cao, Y.; Yu, W.; Ren, W.; Chen, G., An overview of recent progress in the study of distributed multi-agent coordination, IEEE Transactions on Industrial Informatics, 9, 427-438 (2013)
[9] Chang, T. H.; Hong, M.; Wang, X., Multi-agent distributed optimization via inexact consensus ADMM, IEEE Transactions on Signal Processing, 63, 482-497 (2015) · Zbl 1393.90124
[10] Chebotarev, P. Y.; Agaev, R. P., Coordination in multiagent systems and Laplacian spectra of digraphs, Automation and Remote Control, 70, 469-483 (2009) · Zbl 1163.93305
[11] Chen, C.-T., Linear system theory and design (1998), Oxford University Press
[12] Desoer, C. A.; Vidyasagar, M., Feedback systems: Input-output properties (1975), Academic Press: Academic Press NY · Zbl 0327.93009
[13] Franklin, G. F.; Powell, J. D.; Emami-Naeini, A., Feedback control of dynamic systems (2010), Pearson Higher Education: Pearson Higher Education NJ
[14] Gharesifard, B.; Cortés, J., Distributed continuous-time convex optimization on weight-balanced digraphs, IEEE Transactions on Automatic Control, 59, 781-786 (2014) · Zbl 1360.90257
[15] Girard, A.; Pappas, G. J., Hierarchical control system design using approximate simulation, Automatica, 45, 566-571 (2009) · Zbl 1158.93301
[16] Golnaraghi, F.; Kuo, B. C., Automatic control systems (2009), Wiley
[17] Guo, J.; Hug, G.; Tonguz, O. K., A case for nonconvex distributed optimization in large-scale power systems, IEEE Transactions on Power Systems, 32, 3842-3851 (2017)
[18] Hua, M. D.; Hamel, T.; Morin, P.; Samson, C., Introduction to feedback control of underactuated VTOL vehicles, IEEE Control Systems Magazine, 33, 61-75 (2013) · Zbl 1395.93395
[19] Jadbabaie, A.; Lin, J.; Morse, A. S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transactions on Automatic Control, 48, 988-1001 (2003) · Zbl 1364.93514
[20] Johansson, B., Keviczky, T., Johansson, M., & Johansson, K. H. (2008). Subgradient methods and consensus algorithms for solving convex optimization problems. In Proc. 2008 IEEE conference on decision and control (pp. 4185-4190).
[21] Johansson, B., Rabi, M., & Johansson, M. (2007). A simple peer-to-peer algorithm for distributed optimization in sensor networks. In Proc. 46th IEEE conference on decision and control (pp. 4705-4710).
[22] Khalil, H. K., Nonlinear systems (2002), Prentice-Hall: Prentice-Hall NJ · Zbl 1003.34002
[23] Kia, S. S.; Cortés, J.; Martínez, S., Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication, Automatica, 55, 254-264 (2015) · Zbl 1377.93018
[24] Lewis, F. L.; Zhang, H.; Hengster-Movric, K.; Das, A., Cooperative control of multi-agent systems: Optimal and adaptive design approaches (2014), Springer · Zbl 1417.93015
[25] Li, Z.; Wu, Z.; Li, Z.; Ding, Z., Distributed optimal coordination for heterogeneous linear multiagent systems with event-triggered mechanisms, IEEE Transactions on Automatic Control, 65, 1763-1770 (2020) · Zbl 1533.93483
[26] Li, R.; Yang, G. H., Consensus control of a class of uncertain nonlinear multiagent systems via gradient-based algorithms, IEEE Transactions on Cybernetics, 49, 2085-2094 (2018)
[27] Li, L.; Yu, Y.; Li, X.; Xie, L., Exponential convergence of distributed optimization for heterogeneous linear multi-agent systems (2021), ArXiv Preprint arXiv:2101.04353v1
[28] Liang, S.; Zeng, X.; Hong, Y., Distributed nonsmooth optimization with coupled inequality constraints via modified Lagrangian function, IEEE Transactions on Automatic Control, 63, 1753-1759 (2018) · Zbl 1395.90226
[29] Liu, T.; Jiang, Z. P., Distributed control of multi-agent systems with pulse-width-modulated control inputs, Automatica, 119, Article 119020 pp. (2020) · Zbl 1451.93014
[30] Liu, T.; Qin, Z.; Hong, Y.; Jiang, Z. P., Distributed optimization of nonlinear multi-agent systems: A small-gain approach, IEEE Transactions on Automatic Control (2021)
[31] Lu, J.; Tang, C. Y.; Regier, P. R.; Bow, T. D., Gossip algorithms for convex consensus optimization over networks, IEEE Transactions on Automatic Control, 56, 2917-2923 (2011) · Zbl 1368.90023
[32] Martínez, S.; Cortés, J.; Bullo, F., Motion coordination with distributed information, IEEE Control Systems Magazine, 27, 75-88 (2007)
[33] Nesterov, Y., Introductory lectures on convex optimization: A basic course (2004), Springer · Zbl 1086.90045
[34] Ögren, P.; Fiorelli, E.; Leonard, N., Cooperative control of mobile sensor networks: adaptive gradient climbing in a distributed network, IEEE Transactions on Automatic Control, 49, 1292-1302 (2004) · Zbl 1365.93243
[35] Olfati-Saber, R.; Fax, J. A.; Murray, R. M., Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95, 215-233 (2007) · Zbl 1376.68138
[36] Rabbat, M., & Nowak, R. (2004). Distributed optimization in sensor networks. In Proc. 3rd international symposium on information processing in sensor networks (pp. 20-27).
[37] Rahili, S.; Ren, W., Distributed continuous-time convex optimization with time-varying cost functions, IEEE Transactions on Automatic Control, 62, 1590-1605 (2017) · Zbl 1366.93212
[38] Ram, S. S., Nedić, A., & Veeravalli, V. V. (2007). Stochastic incremental gradient descent for estimation in sensor networks. In Proc. 2007 asilomar conference on signals, systems, and computers (pp. 582-586).
[39] Ren, W.; Beard, R., Distributed consensus in multi-vehicle cooperative control: Theory and applications (2008), Springer · Zbl 1144.93002
[40] Russell, R. A., Comparing search algorithms for robotic underground chemical source location, Autonomous Robots, 38, 49-63 (2015)
[41] Tang, Y.; Deng, Z.; Hong, Y., Optimal output consensus of high-order multiagent systems with embedded technique, IEEE Transactions on Cybernetics, 49, 1768-1779 (2019)
[42] Wang, J., & Elia, N. (2010). Control approach to distributed optimization. In Proc. 48th annual allerton conference on communication, control, and computing (pp. 557-561).
[43] Wang, X.; Hong, Y.; Ji, H., Distributed optimization for a class of nonlinear multiagent systems with disturbance rejection, IEEE Transactions on Cybernetics, 46, 1655-1666 (2016)
[44] Wei, Y.; Fang, H.; Zeng, X.; Chen, J.; Pardalos, P., A smooth double proximal primal-dual algorithm for a class of distributed nonsmooth optimization problems, IEEE Transactions on Automatic Control, 65, 1800-1806 (2020) · Zbl 07256304
[45] Xie, Y.; Lin, Z., Global optimal consensus for higher-order multi-agent systems with bounded controls, Automatica, 99, 301-307 (2019) · Zbl 1406.93038
[46] Yang, S.; Liu, Q.; Wang, J., A multi-agent system with a proportional-integral protocol for distributed constrained optimization, IEEE Transactions on Automatic Control, 62, 3461-3467 (2017) · Zbl 1370.90259
[47] Zhang, Y., & Hong, Y. (2015). Distributed optimization design for high-order multi-agent systems. In Proceedings of the 34th Chinese control conference (pp. 7251-7256).
[48] Zhang, F.; Leonard, N. E., Cooperative filters and control for cooperative exploration, IEEE Transactions on Automatic Control, 55, 650-663 (2010) · Zbl 1368.93736
[49] Zhang, J., Liu, L., & Ji, H. (2020). Exponential convergence of distributed optimal coordination for linear multi-agent systems over general digraphs. In Proceedings of the 39th Chinese control conference (pp. 5047-5051).
[50] Zhao, Y.; Liu, Y.; Wen, G.; Chen, G., Distributed optimization of linear multiagent systems: edge- and node-based adaptive designs, IEEE Transactions on Automatic Control, 62, 3602-3609 (2017) · Zbl 1370.93153
[51] Zhu, M.; Martínez, S., On distributed convex optimization under inequality and equality constraints, IEEE Transactions on Automatic Control, 57, 151-164 (2012) · Zbl 1369.90129
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.