×

Event-triggered sliding mode based consensus tracking in second order heterogeneous nonlinear multi-agent systems. (English) Zbl 1405.93062

Summary: This work targets the problem of leader following consensus in heterogeneous multi-agent systems described by second order nonlinear dynamics. The controller proposed in the study is an event-based sliding mode controller. Synthesis of the controller has been partitioned into two parts – a finite time consensus problem and an event-based control mechanism. In the first part, the leader following heterogeneous multi-agents of second order having inherent nonlinear dynamics have been addressed and a novel sliding mode reaching law based on inverse sine hyperbolic function has been designed to drive the agents towards consensus. In the second part, an event-based implementation of the control law has been incorporated to minimize computational load on the computational device equipped with the agents and reduce energy expenditure. The triggering rule proposed in this work is dynamic and taking samples respecting this rule ascertains that the desired closed-loop performance of the system is not compromised while exhibiting robustness and high efficacy. The advantage of using such a scheme, i.e., an event-based sliding mode controller is rooted in the robustness capabilities of sliding mode controller and reducing computational expenses via event-based mechanisms. Numerical simulations and mathematical foundations confirm the effectuality of the controller proposed in this study.

MSC:

93B12 Variable structure systems
93C65 Discrete event control/observation systems
93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
93B50 Synthesis problems
93B35 Sensitivity (robustness)
93C10 Nonlinear systems in control theory
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory

Software:

Boids
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Sinha, A.; Mishra, R. K., Consensus in first order nonlinear heterogeneous multi-agent systems with event-based sliding mode control, International Journal of Control (2018)
[2] Anta, A.; Tabuada, P., To sample or not to sample: Self-triggered control for nonlinear systems, IEEE Trans. Autom. Control, 55, 9, 2030-2042 (2010) · Zbl 1368.93355
[3] Antunes, D.; Khashooei, B. A., Consistent dynamic event-triggered policies for linear quadratic control, IEEE Trans. Control Netw. Syst., PP, 99, 1 (2017)
[4] Astholfi, A.; Marconi, L., Analysis and Design of Nonlinear Control Systems (In Honour of Alberto Isidori) (2007), Springer- Verlag
[5] K.J. Aström, Event Based Control, Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 127-147.; K.J. Aström, Event Based Control, Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 127-147.
[6] Astrom, K. J.; Bernhardsson, B. M., Comparison of Riemann and Lebesgue sampling for first order stochastic systems, Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2, 2011-2016vol.2 (2002)
[7] (Bartolini, G.; Fridman, L.; Pisano, A.; Usai, E., Modern Sliding Mode Control Theory (2008), Springer-Verlag: Springer-Verlag Berlin Heidelberg) · Zbl 1140.93005
[8] Behera, A. K.; Bandyopadhyay, B., Event based robust stabilization of linear systems, Proceedings of the 40th Annual Conference of the IEEE Industrial Electronics Society, IECON 2014, 133-138 (2014)
[9] Bollobas, B., Modern Graph Theory (1998), Springer- Verlag · Zbl 0902.05016
[10] Chartrand, G.; Lesniak, L.; Zhang, P., Graphs & Digraphs, Sixth Edition. Graphs & Digraphs, Sixth Edition, Textbooks in Mathematics (2015), CRC Press- Taylor and Francis Group
[11] Chung, F. R.K., Spectral Graph Theory, CBMS Regional Conference Series in Mathematics, 92 (1997), AMS and CBMS · Zbl 0867.05046
[12] Dávila, J., Distributed tracking of first order systems using second-order sliding modes, IFAC Proc. Vol., 47, 3, 1392-1397 (2014)
[13] Deo, N., Graph Theory with Applications to Engineering and Computer Science (Prentice Hall Series in Automatic Computation) (1974), Prentice-Hall, Inc.: Prentice-Hall, Inc. Upper Saddle River, NJ, USA · Zbl 0285.05102
[14] Dong, Y.; Huang, J., A leader-following rendezvous problem of double integrator multi-agent systems, Automatica, 49, 5, 1386-1391 (2013) · Zbl 1319.93005
[15] Emel’yanov, S. V.; Korovin, S. K.; Levant, A., High-order sliding modes in control systems, Comput. Math. Model., 7, 3, 294-318 (1996)
[16] E. Garcia, Y. Cao, D.W. Casbeer, An event-triggered control approach for the leader-tracking problem with heterogeneous agents, Int. J. Control1-13. doi:10.1080/00207179.2017.1312668; E. Garcia, Y. Cao, D.W. Casbeer, An event-triggered control approach for the leader-tracking problem with heterogeneous agents, Int. J. Control1-13. doi:10.1080/00207179.2017.1312668 · Zbl 1390.93526
[17] Ge, X.; Han, Q. L., Distributed formation control of networked multi-agent systems using a dynamic event-triggered communication mechanism, IEEE Trans. Ind. Electron., PP, 99, 1 (2017)
[18] Girard, A., Dynamic event generators for event-triggered control systems, CoRR, abs/1301.2182 (2013)
[19] Gross, J. L.; Yellen, J.; Zhang, P., Handbook of Graph Theory, Second Edition. Handbook of Graph Theory, Second Edition, Discrete Mathematics and Its Applications (2013), CRC Press- Taylor and Francis Group
[20] Guo, M.; Dimarogonas, D. V., Nonlinear consensus via continuous, sampled, and aperiodic updates, Int. J. Control, 86, 4, 567-578 (2013) · Zbl 1278.93006
[21] Hayakawa, T.; Matsuzawa, T.; Hara, S., Formation control of multi-agent systems with sampled information-relationship between information exchange structure and control performance -, Proceedings of the 45th IEEE Conference on Decision and Control, 4333-4338 (2006)
[22] Khalil, H. K., Nonlinear Systems, Third Edition (2002), Prentice-Hall, Inc.: Prentice-Hall, Inc. Upper Saddle River, NJ, USA
[23] Khoo, S.; Xie, L.; Man, Z., Robust finite-time consensus tracking algorithm for multirobot systems, IEEE/ASME Trans. Mechatron., 14, 2, 219-228 (2009)
[24] M. Lemmon, Event-Triggered Feedback in Control, Estimation, and Optimization, Springer London, London, pp. 293-358.; M. Lemmon, Event-Triggered Feedback in Control, Estimation, and Optimization, Springer London, London, pp. 293-358. · Zbl 1216.93055
[25] Li, H.; Liao, X.; Huang, T.; Zhu, W., Event-triggering sampling based leader-following consensus in second-order multi-agent systems, IEEE Trans. Autom. Control, 60, 7, 1998-2003 (2015) · Zbl 1360.93031
[26] Li, Z.; Duan, Z.; Lewis, F. L., Distributed robust consensus control of multi-agent systems with heterogeneous matching uncertainties, Automatica, 50, 3, 883-889 (2014) · Zbl 1298.93026
[27] Liu, C.-L.; Tian, Y.-P., Formation control of multi-agent systems with heterogeneous communication delays, Int. J. Syst. Sci., 40, 6, 627-636 (2009) · Zbl 1291.93013
[28] Liu, N.; Ling, R.; Huang, Q.; Zhu, Z., Second-order super-twisting sliding mode control for finite-time leader-follower consensus with uncertain nonlinear multiagent systems, Math. Probl. Eng., 2015, 8 (2015) · Zbl 1394.93053
[29] Majumder, T.; Mishra, R. K.; Sinha, A.; Singh, S. S.; Sahu, P. K., Congestion control in cognitive radio networks with event-triggered sliding mode, AEU - Int. J. Electron. Commun., 90, 155-162 (2018)
[30] Mazo, M.; Tabuada, P., Decentralized event-triggered control over wireless sensor/actuator networks, IEEE Trans. Autom. Control, 56, 10, 2456-2461 (2011) · Zbl 1368.93358
[31] Mondal, S.; Su, R.; Xie, L., Heterogeneous consensus of higher-order multi-agent systems with mismatched uncertainties using sliding mode control, Int. J. Robust Nonlinear Control, 27, 13, 2303-2320 (2017) · Zbl 1371.93012
[32] A. Msaddek, A. Gaaloul, F. M’sahli, Output Feedback Robust Exponential Higher Order Sliding Mode Control, Springer Singapore, Singapore, pp. 53-72.; A. Msaddek, A. Gaaloul, F. M’sahli, Output Feedback Robust Exponential Higher Order Sliding Mode Control, Springer Singapore, Singapore, pp. 53-72.
[33] Olfati-Saber, R.; Fax, J. A.; Murray, R. M., Consensus and cooperation in networked multi-agent systems, Proc. IEEE, 95, 1, 215-233 (2007) · Zbl 1376.68138
[34] Peymani, E.; Grip, H. F.; Saberi, A.; Wang, X.; Fossen, T. I., H∞ almost output synchronization for heterogeneous networks of introspective agents under external disturbances, Automatica, 50, 4, 1026-1036 (2014) · Zbl 1298.93031
[35] F. Plestan, V. Brégeault, A. Glumineau, Y. Shtessel, E. Moulay, Advances in High Order and Adaptive Sliding Mode Control-Theory and Applications, Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 465-492.; F. Plestan, V. Brégeault, A. Glumineau, Y. Shtessel, E. Moulay, Advances in High Order and Adaptive Sliding Mode Control-Theory and Applications, Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 465-492.
[36] Ramm, A. G.; Hoang, N. S., Dynamical Systems Method and Applications: Theoretical Developments and Numerical Examples (2011), Wiley
[37] Ren, W.; Beard, R. W., Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE Trans. Autom. Control, 50, 5, 655-661 (2005) · Zbl 1365.93302
[38] Ren, W.; Beard, R. W.; Atkins, E. M., Information consensus in multivehicle cooperative control, IEEE Control Syst., 27, 2, 71-82 (2007)
[39] Reynolds, C. W., Flocks, herds and schools: A distributed behavioral model, (SIGGRAPH ’87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques. SIGGRAPH ’87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques, Anaheim, California (1987)), 25-34
[40] Rezaei, M. H.; Menhaj, M. B., Stationary average consensus for high-order multi-agent systems, IET Control Theory Appl., 11, 5, 723-731 (2017)
[41] Shi, D.; Shi, L.; Chen, T., Event Based State Estimation- A Stochastic Perspective (2016), Springer, Cham · Zbl 1331.62010
[42] Sinha, A.; Kaur, R.; Kumar, R.; Bhondekar, A. P., A cooperative control framework for odor source localization by multi-agent systems (2017), https://hal.archives-ouvertes.fr/hal-01660037. Working paper or preprint
[43] Sinha, A.; Kumar, R.; Kaur, R.; Bhondekar, A. P., Consensus based odour source localisation by multiagent systems, IEEE Transactions on Cybernetics, 1-10 (2018)
[44] Sinha, A.; Kaur, R.; Kumar, R.; Bhondekar, A. P., Cooperative control of multi-agent systems to locate source of an odor, CoRR (2017)
[45] Sinha, A.; Mishra, R. K., Smooth sliding mode controller design for robotic arm, Proceedings of the 2013 International Conference on Control, Automation, Robotics and Embedded Systems (CARE), 1-5 (2013)
[46] Sinha, A.; Mishra, R. K., Nonlinear autonomous altitude control of a miniature helicopter UAV based on sliding mode methodology, Int. J. Electron. Commun. Technol., 6, 1 (2015)
[47] Sinha, A.; Mishra, R. K., Robust altitude tracking of a miniature helicopter UAV based on sliding mode, Proceedings of the 2015 International Conference on Innovations in Information, Embedded and Communication Systems (ICIIECS), 1-6 (2015)
[48] Sinha, A.; Mishra, R. K., Control of a nonlinear continuous stirred tank reactor via event triggered sliding modes, Chem. Eng. Sci., 187, 52-59 (2018)
[49] Sinha, A.; Mishra, R. K., Temperature regulation in a continuous stirred tank reactor using event triggered sliding mode control, IFAC-PapersOnLine, 51, 1, 401-406 (2018)
[50] Sinha, A.; Mishra, R. K.; Jaiswal, S., Robust and smooth nonlinear control of an industrial robot for automated pick and place, Proceedings of the 2015 International Conference on Computing Communication Control and Automation, 1-4 (2015)
[51] Sinha, A.; Prasoon, P.; Bharadwaj, P. K.; Ranasinghe, A. C., Nonlinear autonomous control of a two-wheeled inverted pendulum mobile robot based on sliding mode, Proceedings of the 2015 International Conference on Computational Intelligence and Networks, 52-57 (2015)
[52] Su, Y.; Huang, J., Stability of a class of linear switching systems with applications to two consensus problems, IEEE Trans. Autom. Control, 57, 6, 1420-1430 (2012) · Zbl 1369.93387
[53] Tabuada, P., Event-triggered real-time scheduling of stabilizing control tasks, IEEE Trans. Autom. Control, 52, 9, 1680-1685 (2007) · Zbl 1366.90104
[54] Tallapragada, P.; Chopra, N., On event triggered tracking for nonlinear systems, IEEE Trans. Autom. Control, 58, 9, 2343-2348 (2013) · Zbl 1369.93256
[55] Utkin, V. I., Sliding Modes in Control and Optimization (1992), Springer · Zbl 0748.93044
[56] Wang, Q.; Wu, M.; Huang, Y.; Wang, L., Formation control of heterogeneous multi-robot systems, IFAC Proc. Vol., 41, 2, 6596-6601 (2008)
[57] Wang, X.; Yadav, V.; Balakrishnan, S. N., Cooperative UAV formation flying with obstacle/collision avoidance, IEEE Tran. Control Syst. Technol., 15, 4, 672-679 (2007)
[58] Weihua, Z.; Go, T. H., Robust decentralized formation flight control, Int. J. Aerosp. Eng., 2011 (2011)
[59] Wen, G.; Duan, Z.; Chen, G.; Yu, W., Consensus tracking of multi-agent systems with Lipschitz-type node dynamics and switching topologies, IEEE Trans. Circuits Syst. I: Regul. Pap., 61, 2, 499-511 (2014) · Zbl 1468.93037
[60] Xue, D.; Yao, J.; Chen, G.; l. Yu, Y., Formation control of networked multi-agent systems (brief paper), IET Control Theory Appl., 4, 10, 2168-2176 (2010)
[61] Su, Y.; Huang, J., Stability of a class of linear switching systems with applications to two consensus problems, Proceedings of the 2011 American Control Conference, 1446-1451 (2011)
[62] Yan, X.-G.; Spurgeon, S. K.; Edwards, C., Variable Structure Control of Complex Systems (2017), Springer
[63] Young, K. D.; Utkin, V. I.; Ozguner, U., A control engineer’s guide to sliding mode control, IEEE Trans. Control Syst. Technol., 7, 3, 328-342 (1999)
[64] Yu, W.; Chen, G.; Cao, M., Consensus in directed networks of agents with nonlinear dynamics, IEEE Trans. Autom. Control, 56, 6, 1436-1441 (2011) · Zbl 1368.93015
[65] Yu, W.; Chen, G.; Ren, W.; Kurths, J.; Zheng, W. X., Distributed higher order consensus protocols in multiagent dynamical systems, IEEE Trans. Circuits Syst. I: Regul. Pap., 58, 8, 1924-1932 (2011) · Zbl 1468.93044
[66] Zak, S. H., Systems and Control (2003), Oxford University Press: Oxford University Press 198 Madison Avenue, New York, New York, 10016
[67] Zheng, Y.; Wang, L., Distributed consensus of heterogeneous multi-agent systems with fixed and switching topologies, Int. J. Control, 85, 12, 1967-1976 (2012) · Zbl 1253.93008
[68] Zheng, Y.; Zhu, Y.; Wang, L., Consensus of heterogeneous multi-agent systems, IET Control Theory Appl., 5, 16, 1881-1888 (2011)
[69] Zhou, Y.; Yu, X.; Sun, C.; Yu, W., Higher order finite-time consensus protocol for heterogeneous multi-agent systems, Int. J. Control, 88, 2, 285-294 (2015) · Zbl 1328.93045
[70] Zhu, W.; Jiang, Z.-P.; Feng, G., Event-based consensus of multi-agent systems with general linear models, Automatica, 50, 2, 552-558 (2014) · Zbl 1364.93489
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.