AIMS Mathematics, 2020, 5(1): 587-602. doi: 10.3934/math.2020039.

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Adaptive neural network control for marine surface vehicles platoon with input saturation and output constraints

1 Department of Marine Engineering, Dalian Maritime University, 116026, China
2 College of Automation, Harbin Engineering University, 150001, China

This paper addresses the decentralized problem for marine surface vessels (MSVs) in the presence of unknown unmodeled nonlinear dynamics, time-varying external disturbances and input saturations. First, platoon formation is proceeded by using line-of-sight (LOS) guidance. Since each marine vehicle can only acquire information from its immediate predecessor, a symmetric barrier Lyapunov function (BLF) is employed to guarantee the formation errors constrained within a certain range such that leaders and followers can preserve the predefined information structure and ensure the correct steady-state regime. Next, due to the superior approximation capability of an adaptive neural network (NN), we propose a BLF-based controller to deal with the model uncertainties. Further, an auxiliary design system is introduced to compensate for the effect of input saturation. Finally, the uniform ultimate boundedness of all the state errors can be proved and simulation examples are presented to illustrate the effectiveness of the proposed method.
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Keywords platoon control; marine surface vessels; adaptive neural network control; barrier Lyapunov function; input saturation

Citation: Xiaoling Liang, Chen Xu, Duansong Wang. Adaptive neural network control for marine surface vehicles platoon with input saturation and output constraints. AIMS Mathematics, 2020, 5(1): 587-602. doi: 10.3934/math.2020039


  • 1. Y. Liu, Z. Geng, Finite-time optimal formation tracking control of vehicles in horizontal plane, Nonlinear Dynam., 76 (2014), 481-495.    
  • 2. T. P. Nascimento, L. F. S. Costa, A. G. S. Conceicão, et al. Nonlinear model predictive formation control: An iterative weighted tuning approach, J. Intell. Robot. Syst., 80 (2015), 441-454.    
  • 3. Q. Wang, Y. Wang, H. Zhang, The formation control of multi-agent systems on a circle, IEEE/CAA J. Autom. Sin., 5 (2016), 148-154.
  • 4. B. Das, B. Subudhi, B. B. Pati, Cooperative formation control of autonomous underwater vehicles: An overview, Int. J. Autom. comput., 13 (2016), 199-225.    
  • 5. S. S. Stankovic, M. J. Stanojevic, D. D. Siljak, Decentralized overlapping control of a platoon of vehicles, IEEE T. Contr. Syst. T., 8 (2000), 816-832.    
  • 6. H. Li, Y. Shi, W. Yan, Distributed receding horizon control of constrained nonlinear vehicle formations with guaranteed γ-gain stability, Automatica, 68 (2016), 148-154.    
  • 7. S. J. Yoo, B. S. Park, Guaranteed performance design for distributed bounded containment control of networked uncertain underactuated surface vessels, J. Franklin I., 354 (2017), 1584-1602.    
  • 8. Q. Hou, J. Dong, Adaptive fuzzy reliable control for switched uncertain nonlinear systems based on closed-loop reference model, Fuzzy Set. Syst., DOI:
  • 9. W. He, Z. Yin, C. Sun, Adaptive neural network control of a marine vessel with constraints using the asymmetric barrier Lyapunov function, IEEE T. Cybernetics, 47 (2016), 1641-1651.
  • 10. Z. Peng, D. Wang, Z. Chen, et al. Adaptive dynamic surface control for formations of autonomous surface vehicles with uncertain dynamics, IEEE T. Contr. Syst. T., 21 (2012), 513-520.
  • 11. L. Chen, C. Li, Y. Sun, et al. Distributed finite-time tracking control for multiple uncertain EulerLagrange systems with input saturations and error constraints, IET Contr. Theory Appl., 13 (2018), 123-133.
  • 12. S. Dai, S. He, H. Lin, et al. Platoon formation control with prescribed performance guarantees for USVs, IEEE T. Ind. Electron., 65 (2018), 4237-4246.    
  • 13. E. Rimon, D. E. Koditschek, Exact robot navigation using artificial potential functions, IEET T. Robotic. Autom., 8 (1992): 501-518.
  • 14. C. P. Bechlioulis, G. A. Rovithakis, Robust adaptive control of feedback linearizable MIMO nonlinear systems with prescribed performance, IEEE T. Automat. Contr., 53 (2008), 2090-2099.    
  • 15. J. Na, Q. Chen, X. Ren, et al. Adaptive prescribed performance motion control of servo mechanisms with friction compensation, IEEE T. Ind. Electron., 61 (2013), 486-494.
  • 16. E. G. Gilbert, I. Kolmanovsky, K. T. Tan, Nonlinear control of discrete-time linear systems with state and control constraints: A reference governor with global convergence properties, In: Proceedings of 1994 33rd IEEE Conference on Decision and Control, IEEE, 1 (1994), 144-149.    
  • 17. E. Gilbert, I. Kolmanovsky, Nonlinear tracking control in the presence of state and control constraints: A generalized reference governor, Automatica, 38 (2002), 2063-2073.    
  • 18. D. Li, G. Ma, C. Li, et al. Distributed attitude coordinated control of multiple spacecraft with attitude constraints, IEEE T. Aero. Elec. Syst., 54 (2018): 2233-2245.
  • 19. K. P. Tee, S. S. Ge, E. H. Tay, Barrier Lyapunov functions for the control of output-constrained nonlinear systems, Automatica, 45 (2009), 918-927.    
  • 20. B. S. Park, S. J. Yoo, An error transformation approach for connectivity-preserving and collisionavoiding formation tracking of networked uncertain underactuated surface vessels, IEEE T. Cybernetics, 49 (2018), 2955-2966.
  • 21. Z. Zhao, W. He, S. S. Ge, Adaptive neural network control of a fully actuated marine surface vessel with multiple output constraints, IEEE T. Contr. Syst. T., 22 (2014), 1536-1543.    
  • 22. B. Zhou, X. Yang, Global stabilization of the multiple integrators system by delayed and bounded controls, IEEE T. Automat. Contr., 61 (2015), 4222-4228.
  • 23. X. Liang, M. Hou, G. Duan, Adaptive dynamic surface control for integrated missile guidance and autopilot in the presence of input saturation, J. Aerospace Eng., 28 (2014), 04014121.
  • 24. W. He, Y. Dong, C. Sun, Adaptive neural impedance control of a robotic manipulator with input saturation, IEEE T. Syst. Man Cy. S., 46 (2015), 334-344.
  • 25. H. Wang, X. Liu, K. Liu, Adaptive neural data-based compensation control of non-linear systems with dynamic uncertainties and input saturation, IET Contr. Theory Appl., 9 (2015), 1058-1065.    
  • 26. D. Q. Mayne, J. B. Rawlings, C. V. Rao, et al. Constrained model predictive control: Stability and optimality, Automatica, 36 (2000), 789-814.    
  • 27. X. Liang, M. Hou, H. Guo, A continuous predictive approach based on backstepping with application to integrated guidance and control design, In: 35th Chinese Control Conference, IEEE, 2016, 10870-10874.
  • 28. N. Ji, J. Liu, Vibration control for a flexible satellite with input constraint based on Nussbaum function via backstepping method, Aerosp. Sci. Technol., 77 (2018), 563-572.    
  • 29. Q. Zhou, L. Wang, C. Wu, et al. Adaptive fuzzy control for nonstrict-feedback systems with input saturation and output constraint, IEEE T. Syst. Man Cy. S., 47 (2016), 1-12.
  • 30. Y. Li, S. Tong, T. Li, Adaptive fuzzy output-feedback control for output constrained nonlinear systems in the presence of input saturation, Fuzzy Set. Syst., 248 (2014), 138-155.    
  • 31. L. Sun, W. Huo, Z. Jiao, Adaptive backstepping control of spacecraft rendezvous and proximity operations with input saturation and full-state constraint, IEEE T. Ind. Electron., 64 (2016), 480-492.
  • 32. H. Wang, D. Wang, Z. Peng, Adaptive dynamic surface control for cooperative path following of marine surface vehicles with input saturation, Nonlinear Dynam., 77 (2014), 107-117.    
  • 33. W. He, S. S. Ge, Y. Li, et al. Neural network control of a rehabilitation robot by state and output feedback, J. Intell. Robot. Syst., 80 (2015), 15-31.    
  • 34. D. Li, W. Zhang, W. He, et al. Two-layer distributed formation-containment control of multiple Euler-Lagrange systems by output feedback, IEEE T. Cybernetics, 49 (2018), 675-687.
  • 35. W. Ren, Y. Cao, Distributed Coordination of Multi-Agent Networks: Emergent Problems, Models, and Issues, Springer Science & Business Media, 2010.
  • 36. K. P. Tee, S. S. Ge, Control of fully actuated ocean surface vessels using a class of feedforward approximators, IEEE T. Contr, Syst. T., 14 (2006), 750-756.    


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