Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Cooperative deterministic learning control for a group of homogeneous nonlinear uncertain robot manipulators

  • 155 Accesses

  • 5 Citations


This paper addresses the learning control problem for a group of robot manipulators with homogeneous nonlinear uncertain dynamics, where all the robots have an identical system structure but the reference signals to be tracked differ. The control objective is twofold: to track on reference trajectories and to learn/identify uncertain dynamics. For this purpose, deterministic learning theory is combined with consensus theory to find a common neural network (NN) approximation of the nonlinear uncertain dynamics for a multi-robot system. Specifically, we first present a control scheme called cooperative deterministic learning using adaptive NNs to enable the robotic agents to track their respective reference trajectories on one hand and to exchange their estimated NN weights online through networked communication on the other. As a result, a consensus about one common NN approximation for the nonlinear uncertain dynamics is achieved for all the agents. Thus, the trained distributed NNs have a better generalization capability than those obtained by existing techniques. By virtue of the convergence of partial NN weights to their ideal values under the proposed scheme, the cooperatively learned knowledge can be stored/represented by NNs with constant/converged weights, so that it can be used to improve the tracking control performance without re-adaptation. Numerical simulations of a team of two-degree-of-freedom robot manipulators were conducted to demonstrate the effectiveness of the proposed approach.

This is a preview of subscription content, log in to check access.


  1. 1

    Yuan C, Licht S, He H. Formation learning control of multiple autonomous underwater vehicles with heterogeneous nonlinear uncertain dynamics. IEEE Trans Cybern, 2017, doi: 10.1109/TCYB.2017.2752458

  2. 2

    Yang C, Ganesh G, Haddadin S, et al. Human-like adaptation of force and impedance in stable and unstable interactions. IEEE Trans Robot, 2011, 27: 918–930

  3. 3

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

  4. 4

    Li Z J, Tao P Y, Ge S S, et al. Robust adaptive control of cooperating mobile manipulators with relative motion. IEEE Trans Syst Man Cybern B, 2009, 39: 103–116

  5. 5

    Huang J, Wen C, Wang W, et al. Adaptive finite-time consensus control of a group of uncertain nonlinear mechanical systems. Automatica, 2015, 51: 292–301

  6. 6

    Liu Y J, Lu S, Li D, et al. Adaptive controller design-based ABLF for a class of nonlinear time-varying state constraint systems. IEEE Trans Syst Man Cybern, 2017, 47: 1546–1553

  7. 7

    Liu Y J, Tong S. Barrier Lyapunov functions for Nussbaum gain adaptive control of full state constrained nonlinear systems. Automatica, 2017, 76: 143–152

  8. 8

    Li D P, Li D J, Liu Y J, et al. Approximation-based adaptive neural tracking control of nonlinear MIMO unknown time-varying delay systems with full state constraints. IEEE Trans Cybern, 2017, 47: 3100–3109

  9. 9

    Liu L, Wang Z, Zhang H. Adaptive fault-tolerant tracking control for MIMO discrete-time systems via reinforcement learning algorithm with less learning parameters. IEEE Trans Automat Sci Eng, 2017, 14: 299–313

  10. 10

    Zeinali M, Notash L. Adaptive sliding mode control with uncertainty estimator for robot manipulators. Mech Mach Theor, 2010, 45: 80–90

  11. 11

    He W, Chen Y, Zhao Y. Adaptive neural network control of an uncertain robot with full-state constraints. IEEE Trans Cybern, 2015, 46: 620–629

  12. 12

    Li Z, Deng J, Lu R, et al. Trajectory-tracking control of mobile robot systems incorporating neural-dynamic optimized model predictive approach. IEEE Trans Syst Man Cybern Syst, 2016, 46: 740–749

  13. 13

    Liang X, Wang H, Liu Y H, et al. Adaptive task-space cooperative tracking control of networked robotic manipulators without task-space velocity measurements. IEEE Trans Cybern, 2016, 46: 2386–2398

  14. 14

    Yuan C, Abdelatti M, Dong X, et al. Cooperative deterministic learning control of multi-robot manipulators. In: Proceedings of Chinese Control Conference, Wuhan, 2018. accepted

  15. 15

    Xiao H, Li Z, Chen P C L. Formation control of leader-follower mobile robots’ systems using model predictive control based on neural-dynamic optimization. IEEE Trans Ind Electron, 2016, 63: 5752–5762

  16. 16

    Li Z, Xia Y, Wang D, et al. Neural network-based control of networked trilateral teleoperation with geometrically unknown constraints. IEEE Trans Cybern, 2016, 46: 1051–1064

  17. 17

    Li Z, Yang C, Su C Y, et al. Decentralized fuzzy control of multiple cooperating robotic manipulators with impedance interaction. IEEE Trans Fuzzy Syst, 2015, 23: 1044–1056

  18. 18

    Wang C, Hill D J. Deterministic Learning Theory for Identification, Recognition and Control. Boca Raton: CRC Press, 2009

  19. 19

    Yuan C, Wang C. Persistency of excitation and performance of deterministic learning. Syst Control Lett, 2011, 60: 952–959

  20. 20

    Yuan C, Wang C. Performance of deterministic learning in noisy environments. Neurocomputing, 2012, 78: 72–82

  21. 21

    Yuan C Z, Wang C. Design and performance analysis of deterministic learning of sampled-data nonlinear systems. Sci China Inf Sci, 2014, 57: 032201

  22. 22

    Xu B, Yang C G, Shi Z K. Reinforcement learning output feedback NN control using deterministic learning technique. IEEE Trans Neural Netw Learning Syst, 2014, 25: 635–641

  23. 23

    Wang C, Hill D J. Deterministic learning and rapid dynamical pattern recognition. IEEE Trans Neural Netw, 2007, 18: 617–630

  24. 24

    Chen W, Hua S, Zhang H. Consensus-based distributed cooperative learning from closed-loop neural control systems. IEEE Trans Neural Netw Learn Syst, 2015, 2: 331–345

  25. 25

    Ren W, Beard R W, Atkins E M. Information consensus in multivehicle cooperative control. IEEE Control Syst Mag, 2007, 27: 71–82

  26. 26

    Ni W, Cheng D. Leader-following consensus of multi-agent systems under fixed and switching topologies. Syst Control Lett, 2010, 59: 209–217

  27. 27

    Wang C, Hill D J. Learning from neural control. IEEE Trans Neural Netw, 2006, 17: 130–146

  28. 28

    Shilnikov L P, Shilnikov A L, Turaev D V, et al. Methods of Qualitative Theory in Nonlinear Dynamics. Singapore: World Scientific, 2001

  29. 29

    Olfati-Saber R, Fax J A, Murray R M. Consensus and cooperation in networked multi-agent systems. Proc IEEE, 2007, 95: 215–233

  30. 30

    Dai S L, Wang C, Luo F. Identification and learning control of ocean surface ship using neural networks. IEEE Trans Ind Inf, 2012, 8: 801–810

  31. 31

    Yuan C, He H, Wang C. Cooperative deterministic learning-based formation control for a group of nonlinear uncertain mechanical systems. IEEE Trans Ind Inf, 2018, doi: 10.1109/TII.2018.2792455

  32. 32

    Jadbabaie A, Jie L A, Morse A S. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Automat Contr, 2003, 48: 988–1001

  33. 33

    Vicsek T, Czir´ ok A, Ben-Jacob E, et al. Novel type of phase transition in a system of self-driven particles. Phys Rev Lett, 1995, 75: 1226–1229

  34. 34

    Khalil H. Nonlinear Systems. Upper Saddle River: Prentice-Hall, 2002

  35. 35

    Swaroop D, Hedrick J K, Yip P P, et al. Dynamic surface control for a class of nonlinear systems. IEEE Trans Automat Contr, 2000, 45: 1893–1899

  36. 36

    Xu B, Shi Z, Yang C, et al. Composite neural dynamic surface control of a class of uncertain nonlinear systems in strict-feedback form. IEEE Trans Cybern, 2014, 44: 2626–2634

Download references


This work was supported by National Natural Science Foundation of China (Grant No. 61773194) and Science and Technology Project of Longyan City (Grant No. 2017LY69).

Author information

Correspondence to Chengzhi Yuan.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Abdelatti, M., Yuan, C., Zeng, W. et al. Cooperative deterministic learning control for a group of homogeneous nonlinear uncertain robot manipulators. Sci. China Inf. Sci. 61, 112201 (2018). https://doi.org/10.1007/s11432-017-9363-y

Download citation


  • cooperative deterministic learning
  • multi-robot manipulators
  • neural networks
  • adaptive control
  • multi-agent systems