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Distributed Finite-Time Integral Sliding-Mode Control for Multi-Agent Systems with Multiple Disturbances Based on Nonlinear Disturbance Observers

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Abstract

This paper proposes a finite-time consensus control algorithm based on nonlinear integral sliding-mode control for second-order multi-agent systems (MASs) with mismatched and matched disturbances. Firstly, a nonlinear finite-time disturbance observer is established to estimate the states and mismatched disturbances of the agent. Secondly, a dynamic integral sliding-mode (ISM) surface is designed by employing the estimates of mismatched disturbances. Then, based on the designed ISM and disturbance observer, the discontinuous or continuous campsite control protocols are respectively developed to guarantee the consensus for MASs in finite time with active anti-disturbance control. Finally, numerical simulation results illustrate the effectiveness of the proposed consensus control algorithm.

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References

  1. Qin L, He X, and Zhou D, Distributed proportion-integration-derivation formation control for second-order multi-agent systems with communication time delays, Neurocomputing, 2017, 267: 271–282.

    Article  Google Scholar 

  2. Yang H Y, Zhang Z, and Zhang S, Consensus of second-order multi-agent systems with exogenous disturbances, International Journal of Robust & Nonlinear Control, 2011, 21(9): 945–956.

    Article  MathSciNet  MATH  Google Scholar 

  3. Sun Y, Wang Y, and Zhao D, Flocking of multi-agent systems with multiplicative and independent measurement noises, Physica A Statistical Mechanics & Its Applications, 2015, 440(60): 81–89.

    Article  MathSciNet  MATH  Google Scholar 

  4. Lin P, Ren W, and Song Y, Distributed multi-agent optimization subject to nonidentical constraints and communication delays, Automatica, 2016, 65: 120–131.

    Article  MathSciNet  MATH  Google Scholar 

  5. Wang X, Liu X, She K, et al., Pinning impulsive synchronization of complex dynamical networks with various time-varying delay sizes, Nonlinear Analysis Hybrid Systems, 2017, 26: 307–318.

    Article  MathSciNet  MATH  Google Scholar 

  6. Yang H, Zhu Z, and Zhang S, Consensus of second-order delayed multi-agent systems with leader-following, European Journal of Control, 2010, 16(2): 188–199.

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhang G, Deng Y, Zhang W, et al., Novel DVS guidance and path-following control for under-actuated ships in presence of multiple static and moving obstacles, Ocean Engineering, 2018, 170(11): 100–110.

    Article  Google Scholar 

  8. Chen Y, Ai X, and Zhang Y, Spherical formation tracking control for second-order agents with unknown general flowfields and strongly connected topologies, International Journal of Robust and Nonlinear Control, 2019, 29(11): 3715–3736.

    Article  MathSciNet  MATH  Google Scholar 

  9. Chen Y, Wang Z, Zhang Y, et al., A geometric extension design for spherical formation tracking control of second-order agents in unknown spatiotemporal flowfields, Nonlinear Dynamics, 2017, 88(2): 1173–1186.

    Article  MATH  Google Scholar 

  10. Chen Y, Zhang Y, and Wang Z, An adaptive backstepping design for formation tracking motion in an unknown Eulerian specification flowfield, Journal of the Franklin Institute, 2017, 354(14): 6217–6233.

    Article  MathSciNet  MATH  Google Scholar 

  11. Mo L, Niu Y, and Pan T, Consensus of heterogeneous multi-agent systems with switching jointly-connected interconnection, Physica A Statistical Mechanics & Its Applications, 2015, 427: 132–140.

    Article  MathSciNet  Google Scholar 

  12. Wang Q, Fu J, and Wang J, Fully distributed containment control of high-order multi-agent systems with nonlinear dynamics, Systems & Control Letters, 2017, 99: 33–39.

    Article  MathSciNet  MATH  Google Scholar 

  13. Hu J, Xiao Z, and Zhou Y, Robust consensus tracking control of a second-order leader-follower multi-agent system, IFAC Proceedings Volumes, 2013, 46(20): 130–135.

    Article  Google Scholar 

  14. Li W, Xie L, and Zhang J F, Containment control of leader-following multi-agent systems with Markovian switching network topologies and measurement noises, Automatica, 2015, 51: 263–267.

    Article  MathSciNet  MATH  Google Scholar 

  15. Fu J and Wang J, Robust finite-time containment control of general linear multi-agent systems under directed communication graphs, Journal of the Franklin Institute, 2016, 353(12): 2670–2689.

    Article  MathSciNet  MATH  Google Scholar 

  16. Wang F Y, Yang H Y, Liu Z X, et al., Containment control of leader-following multi-agent systems with jointly-connected topologies and time-varying delays, Neurocomputing, 2017, 260: 341–348.

    Article  Google Scholar 

  17. Yang H, Wang F, and Han F, Containment control of fractional order multi-agent systems with time delays, IEEE/CAA Journal of Automatica Sinica, 2018, 5(3): 727–732.

    Article  MathSciNet  Google Scholar 

  18. Bhat S P and Bernstein D S, Finite-time stability of continuous autonomous systems, SIAM J. Contr. Opti., 2000, 38(3): 751–766.

    Article  MathSciNet  MATH  Google Scholar 

  19. Xiao Q Y, Wu Z H, and Peng L, Fast finite-time consensus tracking of second-order multi-agent systems with a virtual leader, Journal of Networks, 2014, 9(12): 3268–3274.

    Article  Google Scholar 

  20. Wang X, Li S, and Shi P, Distributed finite-time containment control for double-integrator multiagent systems, IEEE Transactions on Cybernetics, 2017, 44(9): 1518–1528.

    Article  Google Scholar 

  21. Cortes J, Finite-time convergent gradient flows with applications to network consensus, Automatica, 2006, 42(11): 1993–2000.

    Article  MathSciNet  MATH  Google Scholar 

  22. Zhang Y and Yang Y, Distributed finite-time tracking control for nonlinear multi-agent systems subject to external disturbances, International Journal of Control, 2013, 86(1): 29–40.

    Article  MathSciNet  MATH  Google Scholar 

  23. Chen G, Yue Y, and Song Y, Finite-time cooperative-tracking control for networked Euler-Lagrange systems, IET Control Theory & Applications, 2013, 7(11): 1487–1497.

    Article  MathSciNet  Google Scholar 

  24. Xiao F, Wang L, Chen J, et al., Finite-time formation control for multiagent systems, Automatica, 2009, 45(11): 2605–2611.

    Article  MathSciNet  MATH  Google Scholar 

  25. Zhang G, Huang C, Zhang X, et al., Practical constrained dynamic positioning control for uncertain ship through the minimal learning parameter technique, IET Control Theory & Applications, 2018, 12(18): 2526–2533.

    Article  Google Scholar 

  26. Lu Y, Zhang G, Sun Z, et al., Adaptive cooperative formation control of autonomous surface vessels with uncertain dynamics and external disturbances, Ocean Engineering, 2018, 167: 36–44.

    Article  Google Scholar 

  27. Yang H, Yang Y, Han F, et al., Containment control of heterogeneous fractional-order multi-agent systems, Journal of the Franklin Institute, 2019, 356(2): 752–765.

    Article  MathSciNet  MATH  Google Scholar 

  28. Zhang G, Tian B, Zhang W, et al., Optimized robust control for industrial unstable process via the mirror-mapping method, ISA Transactions, 2019, 86: 9–17.

    Article  Google Scholar 

  29. Ou L L, Zhang W D, and Yu L, Low-order stabilization of LTI systems with time delay, IEEE Transactions on Automatic Control, 2009, 54(4): 774–787.

    Article  MathSciNet  MATH  Google Scholar 

  30. Lu Y, Zhang G, Sun Z, et al., Robust adaptive formation control of underactuated autonomous surface vessels based on MLP and DOB, Nonlinear Dynamics, 2018, 94(1): 503–519.

    Article  MATH  Google Scholar 

  31. Wang M, Ren X, and Chen Q, Robust tracking and distributed synchronization control of a multi-motor servomechanism with H-infinity performance, ISA Transactions, 2017, 72: 147–160.

    Article  Google Scholar 

  32. Sun Z, Zhang G, Lu Y, et al., Leader-follower formation control of underactuated surface vehicles based on sliding mode control and parameter estimation, ISA Transactions, 2017, 72: 15–24.

    Article  Google Scholar 

  33. Zhao Q, Dong X, Liang Z, et al., Distributed cooperative guidance for multiple missiles with fixed and switching communication topologies, Chinese Journal of Aeronautics, 2017, 30(4): 1570–1581.

    Article  MATH  Google Scholar 

  34. Yang J, Zolotas A, Chen W H, et al., Robust control of nonlinear MAGLEV suspension system with mismatched uncertainties via DOBC approach, ISA Transactions, 2011, 50(3): 389–396.

    Article  Google Scholar 

  35. Li S H, Yang J, Chen W H, et al., Disturbance Observer-Based Control: Methods and Applications, CRC Press, Inc. 2014.

  36. Yang J, Li S H, and Yu X H, Sliding-mode control for systems with mismatched uncertainties via a disturbance observer, IEEE Transactions on Industrial Electronics, 2012, 60(1): 160–169.

    Article  Google Scholar 

  37. Wang X Y, Li S H, and Lam J, Distributed active anti-disturbance output consensus algorithms for higher-order multi-agent systems with mismatched disturbances, Automatica, 2016, 74: 30–37.

    Article  MathSciNet  MATH  Google Scholar 

  38. Mondal S, Su R, and Xie L, Heterogeneous consensus of higher-order multi-agent systems with mismatched uncertainties using sliding mode control, International Journal of Robust and Nonlinear Control, 2016, 27(13): 2303–2320.

    Article  MathSciNet  MATH  Google Scholar 

  39. Zhang Z, Li S, and Luo S, Terminal guidance laws of missile based on ISMC and NDOB with impact angle constraint, Aerospace Science & Technology, 2013, 31(1): 30–41.

    Article  Google Scholar 

  40. Khalil H K, Nonlinear Systems, 3rd Edition, Prentice Hall, New York, 2002.

    MATH  Google Scholar 

  41. Levant A, Higher-order sliding modes, differentiation and output-feedback control, International Journal of Control, 2003, 76(9–10): 924–942.

    Article  MathSciNet  MATH  Google Scholar 

  42. Shtessel Y B, Shkolnikov I A, and Levant A, Smooth second-order sliding modes: Missile guidance application, Automatica, 2007, 43(8): 1470–1476.

    Article  MathSciNet  MATH  Google Scholar 

  43. Davila A, Moreno J A, and Fridman L, Optimal Lyapunov function selection for reaching time estimation of super twisting algorithm, 48th IEEE Conference on Decision and Control (CDC) Held Jointly with 2009 28th Chinese Control Conference, Shanghai, China, 2009, 8405–8410.

  44. Hong Y G, Xu Y S, and Huang J, Finite-time control for robot manipulators, Systems & Control Letters, 2002, 46(4): 243–253.

    Article  MathSciNet  MATH  Google Scholar 

  45. Yu S and Long X, Finite-time consensus for second-order multi-agent systems with disturbances by integral sliding mode, Automatica, 2015, 54: 158–165.

    Article  MathSciNet  MATH  Google Scholar 

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Corresponding author

Correspondence to Hongyong Yang.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 61673200 and 61771231, the Natural Science Foundation of Shandong Province of China under Grant Nos. ZR2018ZC0438 and ZR2017MF010, and Key Research and Development Program of Yantai of China under Grant No. 2019XDHZ085.

This paper was recommended for publication by Editor JIA Yingmin.

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Yang, Y., Liu, F., Yang, H. et al. Distributed Finite-Time Integral Sliding-Mode Control for Multi-Agent Systems with Multiple Disturbances Based on Nonlinear Disturbance Observers. J Syst Sci Complex 34, 995–1013 (2021). https://doi.org/10.1007/s11424-020-9152-6

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  • DOI: https://doi.org/10.1007/s11424-020-9152-6

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