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Neural network-based adaptive output feedback formation control for multi-agent systems

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Abstract

This paper investigates the problem of output feedback formation tracking control for second-order multi-agent systems under an undirected connected graph and in the presence of dynamic uncertainties and bounded external disturbances. Two state tracking error measures (i.e., absolute and relative state tracking errors) are considered for each individual agent in the formation, and linear reduced-order observers are constructed based on the lumped state tracking errors which include absolute and relative state tracking errors. Chebyshev neural networks are used to approximate unknown nonlinear function in the agent dynamics on-line, and the implementation of the basis functions of Chebyshev neural networks depends only on the desired signals. The smooth projection algorithm is applied to guarantee that the estimated parameters remain in some known bounded sets. Numerical simulations are presented to illustrate the performance of the proposed controller.

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References

  1. Chung, S.J., Slotine, J.J.E.: Cooperative robot control and concurrent synchronization of Lagrangian systems. IEEE Trans. Robot. 25, 686–700 (2009)

    Article  Google Scholar 

  2. Balch, T., Arkin, R.C.: Behavior-based formation control for multirobot teams. IEEE Trans. Robot. Autom. 14, 926–939 (1998)

    Article  Google Scholar 

  3. Lewis, M.A., Tan, K.-H.: High precision formation control of mobile robots using virtual structures. Auton. Robots 4, 387–403 (1997)

    Article  Google Scholar 

  4. Ogren, P., Egerstedt, M., Hu, X.: A control Lyapunov function approach to multiagent coordination. IEEE Trans. Robot. Autom. 18, 847–851 (2002)

    Article  Google Scholar 

  5. Giulietti, F., Pollini, L., Innocenti, M.: Autonomous formation flight. IEEE Control Syst. 20, 34–44 (2000)

    Article  Google Scholar 

  6. Stilwell, D.J., Bishop, B.E.: Platoons of underwater vehicles. IEEE Control Syst. 20, 45–52 (2000)

    Article  Google Scholar 

  7. Kang, W., Yeh, H.-H.: Coordinated attitude control of multi-satellite systems. Int. J. Robust Nonlinear Control 12, 185–205 (2002)

    Article  MATH  Google Scholar 

  8. Carpenter, J.R.: Decentralized control of satellite formations. Int. J. Robust Nonlinear Control 12, 141–161 (2002)

    Article  MATH  Google Scholar 

  9. Lawton, J., Beard, R.W.: Synchronized multiple spacecraft rotations. Automatica 38, 1359–1364 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ren, W., Beard, R.W.: Decentralized scheme for spacecraft formation flying via the virtual structure approach. J. Guid. Control Dyn. 27, 73–82 (2004)

    Article  Google Scholar 

  11. Ren, W.: Distributed attitude alignment in spacecraft formation flying. Int. J. Adapt. Control Signal Process. 21, 95–113 (2007)

    Article  MATH  Google Scholar 

  12. Ren, W.: Distributed cooperative attitude synchronization and tracking for multiple rigid bodies. IEEE Trans. Control Syst. Technol. 18, 383–392 (2010)

    Article  Google Scholar 

  13. VanDyke, M.C., Hall, C.D.: Decentralized coordinated attitude control within a formation of spacecraft. J. Guid. Control Dyn. 29, 1101–1109 (2006)

    Article  Google Scholar 

  14. Changa, I., Park, S.-Y., Choi, K.-H.: Decentralized coordinated attitude control for satellite formation flying via the state-dependent Riccati equation technique. Int. J. Non-Linear Mech. 44, 891–904 (2009)

    Article  Google Scholar 

  15. Abdessameud, A., Tayebi, A.: Attitude synchronization of a group of spacecraft without velocity measurements. IEEE Trans. Autom. Control 54, 2642–2648 (2009)

    Article  MathSciNet  Google Scholar 

  16. Scharf, D.P., Hadeagh, F.Y., Ploen, S.R.: A survey of spacecraft formation flying guidance and control. Part II. Control. In: Proceedings of the 2004 American Control Conference, Boston, MA, pp. 2976–2985 (2004)

    Google Scholar 

  17. Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Netw. 2, 359–366 (1989)

    Article  Google Scholar 

  18. Sanner, R.M., Slotine, J.J.E.: Gaussian networks for direct adaptive control. IEEE Trans. Neural Netw. 3, 837–863 (1992)

    Article  Google Scholar 

  19. Wang, L.X., Mendel, J.M.: Fuzzy basis function, universal approximation, and orthogonal least-squares learning. IEEE Trans. Neural Netw. 3, 807–814 (1992)

    Article  Google Scholar 

  20. Lee, T.-T., Jeng, J.-T.: The Chebyshev-polynomials-based unified model neural networks for function approximation. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 28, 925–935 (1998)

    Article  Google Scholar 

  21. Patra, J.C., Kot, A.C.: Nonlinear dynamic system identification using Chebyshev functional link artificial neural networks. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 32, 505–511 (2002)

    Article  Google Scholar 

  22. Hou, Z.G., Cheng, L., Tan, M.: Decentralized robust adaptive control for the multiagent system consensus problem using neural networks. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 39, 636–647 (2009)

    Article  Google Scholar 

  23. Cheng, L., Hou, Z.G., Tan, M., Lin, Y., Zhang, W.: Neural-network-based adaptive leader-following control for multiagent systems with uncertainties. IEEE Trans. Neural Netw. 21, 1351–1358 (2010)

    Article  Google Scholar 

  24. Das, A., Lewis, F.L.: Cooperative adaptive control for synchronization of second-order systems with unknown nonlinearities. Int. J. Robust Nonlinear Control 21, 1509–1524 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  25. Chen, G., Lewis, F.L.: Distributed adaptive tracking control for synchronization of unknown networked Lagrangian systems. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 41, 805–816 (2011)

    Article  Google Scholar 

  26. Dierks, T., Jagannathan, S.: Asymptotic adaptive neural networks tracking control of nonholonomic mobile robot formations. J. Intell. Robot. Syst. 56, 153–176 (2009)

    Article  MATH  Google Scholar 

  27. Zou, A.-M., Kumar, K.D., Hou, Z.-G.: Quaternion-based adaptive output feedback attitude control of spacecraft using Chebyshev neural networks. IEEE Trans. Neural Netw. 21, 1457–1471 (2010)

    Article  Google Scholar 

  28. Zou, A.-M., Kumar, K.D., Hou, Z.-G., Liu, X.: Finite-time attitude tracking control for spacecraft using terminal sliding mode and Chebyshev neural network. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 41, 950–963 (2011)

    Article  Google Scholar 

  29. Godsil, C., Royle, G.: Algebraic Graph Theory. Springer, New York (2001)

    Book  MATH  Google Scholar 

  30. Teel, A.R.: Adaptive tracking with robust stability. In: The 32nd IEEE Conference on Decision and Control, pp. 570–575 (1993)

    Google Scholar 

  31. Yao, B., Tomizuka, M.: Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form. Automatica 33, 893–900 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  32. Narendra, K.S., Annaswamy, A.M.: A new adaptive law for robust adaptation without persistent excitation. IEEE Trans. Autom. Control 32, 134–145 (1987)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Aerospace Engineering, Ryerson University, Toronto, Canada

    An-Min Zou & Krishna Dev Kumar

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  1. An-Min Zou
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  2. Krishna Dev Kumar
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Correspondence to An-Min Zou.

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Zou, AM., Kumar, K.D. Neural network-based adaptive output feedback formation control for multi-agent systems. Nonlinear Dyn 70, 1283–1296 (2012). https://doi.org/10.1007/s11071-012-0533-9

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  • DOI: https://doi.org/10.1007/s11071-012-0533-9

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