Abstract
In this study we consider the distributed output agreement problem in a class of multi-agent dynamic systems with uncertainties. The problem is formulated as a nonlinear servomechanism problem and an adaptive internal model-based controller is used to achieve agreement of the agent outputs using local information. Various agent neighborhood topologies are considered and the performance of the system is verified using simple numerical simulations.
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Notes
- 1.
Here we use the term connected loosely meaning that at least minimum connectivity conditions are satisfied and there are no agents or groups of agents which are disconnected from the rest of the multi-agent system. For example, as mentioned earlier for static unidirectional topology it is sufficient that the interaction topology has a spanning tree.
- 2.
At the time the simulation is stopped, the average interagent distance is very close to zero and continues to decrease.
References
Byrnes, C.I., Priscoli, F.D., Isidori, A., Kang, W.: Structurally stable output regulation of nonlinear systems. Automatica 33(3), 369–385 (1997)
Chen, X., Serrani, A., Özbay, H.: Control of leader-follower formations of terrestrial uavs. In: Proceedings of the 42nd IEEE Conference on Decision and Control, pp. 498–503. Hawaii, USA, Dec 2003
Davison, E.J.: The robust control of a servomechanism problem for linear time-invariant multivariable systems. IEEE Trans. Autom. Control 21(1), 25–34 (1976)
Francis, B.A.: The linear multivariable regulator problem. In: 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes, vol. 15, pp. 873–878 (1976)
Francis, B.A., Wonham, W.M.: The internal model principle of control theory. Automatica 12, 457–465 (1976)
Gazi, V., Fidan, B.: Coordination and control of multi-agent dynamic systems: models and approaches. In: Sahin, E., Spears, W.M., Winfield, A.F.T. (eds.) Proceedings of the SAB06 Workshop on Swarm Robotics, pp. 71–102. Lecture Notes in Computer Science (LNCS) vol. 4433, Springer, Berlin (2007)
Gazi, V.: Formation control of a multi-agent system using nonlinear servomechanism. Int. J. Control 78(8), 554–565 (2005)
Gazi, V.: Output regulation of a class of linear systems with switched exosystems. Int. J. Control 80(10), 1665–1675 (2007)
Gazi, V.: Stability of a discrete-time asynchronous swarm with time-dependent communication links. IEEE Trans. Syst. Man Cybern: Part B 38(1), 267–274 (2008)
Gazi, V., Passino, K.M.: Decentralized output regulation of a class of nonlinear systems. Int. J. Control 79(12), 1512–1522 (2006)
Gazi, V., Passino, K.M.: Swarm Stability and Optimization. Springer, Heidelberg (2011)
Gül, E., Gazi, V.: Adaptive internal model based distributed output agreement in a class of multi-agent dynamic systems. In: Kolemisevska-Gugulovska, T.D., Stankovski, M.J. (eds.) Proceedings of the Special International Conference on Complex Systems: Synergy of Control, Computing, and Communications (COSY 2011), pp. 215–222. The Society for Electronics, Telecommunications, Automation, and Informatics of Macedonia, Skopje, MK, Ohrid, Macedonia, Sept 2011
Gül, E., Gazi, V.: Adaptive internal model based formation control of a class of multi-agent systems with switched exosystems. In: Chinese Control and Decision Conference, pp. 6–13. Taiyuan, China, May 2012
Gül, E., Gazi, V.: Adaptive internal model based formation control of a class of multi-agent systems. In: American Control Conference, pp. 4800–4805. Baltimore, MD, USA, June–July 2010
Huang, J., Lin, C.: On a robust nonlinear servomechanism problem. IEEE Trans. Autom. Control 39(7), 1510–1513 (1994)
Huang, J., Rugh, W.J.: On a nonlinear multivariable servomechanism problem. Automatica 26(6), 963–972 (1990)
Isidori, A., Byrnes, C.I.: Output regulation of nonlinear systems. IEEE Trans. Autom. Control 35(2), 131–140 (1990)
Jadbabaie, A., Lin, J., Morse, A.S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Autom. Control 48(6), 988–1001 (2003)
Khalil, H.K.: Robust servomechanism output feedback controllers for feedback linearizable systems. Automatica 30(10), 1587–1599 (1994)
Kim, H., Shim, H., Seo, J.H.: Output consensus of heterogeneous uncertain linear multi-agent systems. IEEE Trans. Autom. Control 56(1), 200–206 (2011)
Lin, Z., Francis, B., Maggiore, M.: Necessary and sufficient graphial conditions for formation control of unicycles. IEEE Trans. Autom. Control 50(1), 121–127 (2005)
Mahmoud, N.A., Khalil, H.K.: Asymptotic regulation of minimum phase nonlinear systems using output feedback. IEEE Trans. Autom. Control 40(10), 1402–1412 (1996)
Mahmoud, N.A., Khalil, H.K.: Robust control for a nonlinear servomechanism problem. Int. J. Control 66(6), 779–802 (1997)
Marino, R., Tomei, P.: Output regulation for linear systems via adaptive internal model. IEEE Trans. Autom. Control 48(12), 2199–2202 (2003)
Moreau, L.: Stability of multiagent systems with time-dependent communication links. IEEE Tran. Autom. Control 50(2), 169–182 (2005)
Nikiforov, V.O.: Adaptive nonlinear tracking with complete compensation of unknown disturbances. Euro. J. Control 4, 132–139 (1998)
Olfati-Saber, R., Murray, R.M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)
Ren, W., Beard, R.W.: Consensus seeking in multi-agent systems under dynamically changing interaction topologies. IEEE Trans. Autom. Control 50(5), 655–661 (2005)
Şamiloğlu, A.T., Gazi, V., Koku, A.B.: Asynchronous cyclic pursuit. In: S. Nolfi (ed.) Proceedings of 9’th Conference on Simulation of Adaptive Behavior (SAB06), pp. 667–678. Lecture Notes in Artificial Intelligence (LNAI) 4095, Springer, Berlin (2006)
Serrani, A., Isidori, A., Marconi, L.: Semiglobal nonlinear output regulation with adaptive internal model. IEEE Trans. Autom. Control 46(8), 1178–1194 (2001)
Serrani, A., Isidori, A.: Global robust output regulation for a class of nonlinear systems. Syst./Control Lett. 39, 133–139 (1999)
Wieland, P., Allgöwer, F.: An internal model principle for consensus in heterogeneous linear multi-agent systems. In: 1st IFAC Workshop on Estimation and Control in Networked Systems, pp. 7–12. Venice, Italy, Sept 2009
Wieland, P., Allgöwer, F.: An internal model principle for synchronization. In: IEEE International Conference on Control and Automation (ICCA), pp. 285–290. Christchurch, New Zealand, Dec 2009
Wieland, P., Sepulchre, R., Allgöwer, F.: An internal model principle is necessary and sufficient for linear output synchronization. Automatica 47(5), 1068–1074 (2011)
Xiang, J., Wei, W., Li, Y.: Synchronized output regulation of linear networked systems. IEEE Trans. Autom. Control 54(6), 1336–1341 (2009)
Ye, X., Huang, J.: Decentralized adaptive output regulation for a class of large-scale nonlinear systems. IEEE Tran. Autom. Control 48(2), 276–281 (2003)
Acknowledgments
This work was supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) under grant no 109E175.
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Gül, E., Gazi, V. (2016). Adaptive Internal Model-Based Distributed Output Agreement in a Class of Multi-Agent Dynamic Systems. In: Dimirovski, G. (eds) Complex Systems. Studies in Systems, Decision and Control, vol 55. Springer, Cham. https://doi.org/10.1007/978-3-319-28860-4_21
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